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jProwi Philosophical Magazine for July 1912.

COMPLIMENTS OF THE AUTHOR

Studies in the Photometry of Lights of Different Colours.
By Herbert E. Ives.

[Plates III.-V.]

I.

Spectral Luminosity Curves obtained by the Equality of
Brightness Photometer and the Flicker Photometer under
similar conditions.

Synopsis.

Introduction.

1. Difficulties in determination of luminosity in the presence of colour

difference.

2. Existing methods of heterochromatic photometry .

a. Equality of brightness.

b. Visual acuity.

c. Critical frequency.

d. Flicker photometer.

I -J et

150

Mr. H. E. Ives on the

3. Requirements of a good method of measurement,

a. Sensibility.

b. Summation quality.

c. Useful value of quantity measured.

4. Degree to which these requirements are met by existing methods.

Equality of brightness and flicker methods meet requirements
much better than other methods, with apparent advantage
in flicker method of greater sensibility. Different results
obtained by these two methods indicate importance of a com-
parison between them.

5. Physiological factors to be considered.

a. "Purkinje " and. " yellow spot" effects. Pods and cones.

b. Colour blindness.

c. Adaptation .and fatigue.

Spectbal Luminosity Curves as obtained by Flicker and
Equality of Brightness Photometers.

1. Previous Comparisons. Dow, Stuhr, Millar, Wilde.

Apparent differences in the magnitude of Purkinje and yellow
spot effects with the two photometers.

2. Apparatus and Procedwe.

Arrangements for securing monochromatic spectral colours at
various illuminations and with various sizes of the field of
view. Details of measurements.

3. Measurement.

a. Sensibility.

Greater sensibility by the flicker method. Flicker speeds.

b. Reproducibility of measurements.

Greater reproducibility by the flicker method.

c. Effect of changing illumination.

" Purkinje effect " by equality of brightness, reverse effect by
flicker.

d. Effect of changing field size.

" Yellow spot " effect at low illumination by equality of
brightness, reverse of this effect by flicker.

e. Relative positions of flicker and equality of brightness curves.
Nearest each other at high illuminations and with small

fields.

Areas of two kinds of luminosity curves different.
/. Comparative results obtained by different observers.

4. Theoretical Considerations.

Significance of Purkinje and opposite effects. Bearing on theory
of rod and cone action. Insufficiency of present theories.
Future work indicated.

5. Bearing upon Practical Photometry.

Inteoduction.

ANY light may be denned in terms of hue, saturation,
and luminosity. Practical photometry is concerned
primarily with luminosity. But that quality of light cannot
by simple means be separated from the other two. The eye can
equate but cannot appraise. Hence the eye is on uncertain
ground whenever it attempts to compare the luminosities

Photometry of Lights of Different Colours, 151

of lights of different hue or saturation. This difficulty has
long been recognized, and various opinions as to the solva-
bility of the problem have been expressed. Various plans to
accomplish its solution have been proposed. The belief has
been expressed by some that comparison of the luminosities
of two differently coloured lights is no more possible of exact
accomplishment than the exact comparison of a sound with
an odour. Helmholtz declared his lack of confidence in his
own ability to make such comparisons. On the other hand,
some observers have by practice acquired skill and apparent
certainty in heterochromatic photometry. Again, methods
of photometry have been discovered and developed which, in
the process of measurement, evade and perhaps eliminate the
differences in hue and saturation.

By these different methods different criteria for equality of
luminosity are obtained. What are the relations between the
criteria ? Are two coloured lights which are equally bright
as measured by one method, of equal brightness as measured
by another ?

The relative brightness of differently coloured lights is not
constant under all conditions. Physiological factors enter to
a large degree. The u Purkinje effect" is the name given
to the increase of blue sensitiveness at low illumination. The
" yellow spot effect " is the name given to the change in
the relative brightnesses of different colours occurring when
the size of the field of view is changed. To what degree do
these enter in the various methods of colour photometry ?

The advent of high efficiency incandescent lamps and of
new illuminants with wide range of colour, the prospect
of an even greater variety of illuminants in the future,
diverging still further in colour from the present flame and
carbon lamp standards, all render the problem of measuring
the luminosity of lights of various hues one of the most
important in photometry. A complete solution of the problem
can come only through knowledge of the relative behaviour of
each method of comparison under the various conditions known
to affect the relative brightness of different colours. That
knowledge acquired, we may proceed to a process of test and
selection, and so hope to determine that method which meets
to the fullest degree the requirements of a method of
measurement.

The chief obstacle in the way of giving preference to one
method of colour photometry over another is at present our
lack of data. Some forms of flicker photometers have been
compared with some forms of direct comparison photometers.
Spectral luminosity curves for the eye have been derived by
tests of visual acuity, by the flicker photometer, by equality

152

Mr. H. E. Ives on the

of brightness methods, and by the determination of critical
frequency of flicker. But such investigations have been
carried out by different observers, using different conditions
of illumination and different colour standards, with instru-
ments whose dimensions were different in essential particulars.
And frequently some of the most important conditions have
not been stated. Prominent among these should be mentioned
the illumination and the size of the photometric field.

It is the object of the present studies to obtain data for the
solution of this problem. For this purpose comparisons will
be made between the various methods. The different factors
which influence the relative luminosity of colour will be
systematically varied as each method is studied. The same
conditions will, however, be maintained throughout, whereby
satisfactory comparisons of the different methods will be
possible. Attention will be devoted chiefly to the most
promising lines of investigation, and ground covered by
previous workers will not be touched unless coordination
of their work with the present work is found impossible.
Problems incidental to the main questions will be investi-
gated where necessary, but the ultimate object to be held in
view will be the determination of the most satisfactory
method of measuring luminosity where differences of colour
exist.

Existing Methods of Heterochromatic Photometry,

The chief methods of light measurement which have been
applied to differently coloured lights are : —

1. The method of equality of brightness. — The two lights
illuminate the two parts of a photometric field. The relative
intensities of illumination from the two lights are changed
until the two differently coloured fields give a sensation
of equal brightness. The illuminations are then called
equal.

2. The method of visual acuity. — Two illuminations are
equal when the same fineness of detail is just distinguishable
by each.

3. By critical frequency. — Two illuminations are equal
when the flicker produced by rapid alternation of one illumi-
nation with black disappears at the same speed of alternation
as for the other when similarly alternated.

4. The flicker photometer. — Two illuminations are equal
when upon rapidly alternating one with the other no sen-
sation of flicker results, the speed of alternation being such
that the slightest change of either illumination produces a

Photometry of Lights of Different Colours.

153

The Requirements of a Good Method of Measurement.

As a preliminary to an investigation of these methods of
measurement, the requirements necessary to a satisfactory
method should be kept clearly in mind. These are, first, that
the range of possible settings of the measuring instrument shall
be small ; that is, the method shall be as definite as possible.
In the photometry of lights of the same colour, for instance,
the range with a Lummer-Brodhun contrast photometer is
of the order of one per cent. Second, that the quantities to
which values are given by the measurements shall behave
as arithmetical or physical quantities. This involves that
quantities measured as equal to the same thing shall measure
equal to each other, and that the sum of the parts shall be
equal to the whole. This second requirement of a method
of measurement is not one often dwelt upon in the measurement
of purely physical quantities, because such quantities naturally
fulfil the requirement. In dealing with physiological quan-
tities, however, it cannot be assumed without proof that this
is true. As a third requirement in the present case may be
added that the values given to different colours shall represent
as nearly as possible their useful value as light. In explanation
of this last requirement it will suffice to point out that the
first two requirements, which pertain to any method of mea-
surement, would be met by simple measurement of the energy
radiated. Light, however, considered as a sensation, is repre-
sented by very different quantities of energy at different
wave-lengths in the visible and invisible spectrum, and such
a measuremeut would not give a number to the light value.
Or, again, if there exists a fundamental quantity of brightness,
which can only be separated and measured under very special
conditions, this measurement, while perhaps satisfactory to
the psychologist or physiologist, would not satisfy the photo-
metrist, who is interested in light as used for illumination,
even if the underlying real brightness quality is masked by
other qualities such as hue. What is therefore required is
a method of measuring lights of different colours with the
same order of definiteness which pertains to strictly physical
measurements, using units which may be dealt with as
physical quantities, but yet yielding values closely repre-
senting the values of the lights for illumination, for good
seeing, or as producers of the sensation of brightness.

Degree to which these Requirements are met by Existing

Methods.

Comparison of the brightness of two fields of different
colour is a somewhat uncertain and unsatisfactory process.

154

Mr. H. E. Ives on the

The difficulty is largely psychological. A decision must be
formed as to when a certain quality of the two illuminations
is equal, while other inseparable qualities are different. With
a large colour difference, this decision is difficult ; at first
attempt almost impossible. At best, one's settings are apt to
vary over a wide range ; at another time a different decision
may be made, and the average of a set of readings diverge
considerably from the set previously made. With small colour
differences an observer will with practice make quite definite
settings, and his criterion of equality then probably assumes
a fairly constant value. As a method of heterochromatic
photometry, the method of direct comparison is principally
open to objection because of its lack of definiteness of
setting.

As to the second requirement, that the measured light
quantities may be treated as physical quantities, i. e., com-
pared in any order or added to produce their arithmetical
sum, Abney with his colour-patch apparatus has measured
the intensities of several spectral colours separately and then
together, finding practically perfect agreement between the
sum of the intensities and the intensity of the sum. In view
of the difficulty of making exact settings with coloured fields,
those results show remarkable agreement. It is to be regretted,
however, that these measurements were made with such an
inexact instrument as a shadow photometer, that the illumi-
nation from the different colours (an arc spectrum) was very
different, and that the measurements were confined to very
small fields : in short, that they were made under conditions
quite different from ordinary photometry.

As to the method of visual acuity, its chief defect is
extreme lack of definiteness. Properly it should be used
only for determining different orders of illumination. Visual
I acuity varies as the logarithm of the illumination and very
I slowly. For instance, with the best test objects probably a
5 per cent difference in visual acuity represents the limit
of perceptible difference. Study of Koenig's data on the
relation between visual acuity and illumination shows that
this corresponds in the middle region of illumiuation studied
to about 30 per cent, difference in illumination. As a method
of measuring illumination, visual acuity is therefore almost
beneath notice. This is borne out by the work of all
observers; so that while visual acuity may be a correct
measure of good seeing conditions, it is not a method of
photometry. Until, therefore, it shall be proved that the
criterion of good seeing as so determined is very different
from that given by other methods, and much more important.

Pliotometry of Lights of Different Colours. 155

visual acuity would not appear to deserve much attention.
To the writer's knowledge no measurements are on record
which were made to determine whether the arithmetic sum
of two differently coloured illuminations measures equal to
the two illuminations together. One advantage the method
of visual acuity has over that of equality of brightness, is that
by the nature of the criterion two illuminations equal to the
same are assuredly equal to each other. This fact depends
of course on the illuminations not being compared one with
another, but with, as it were, an outside standard of different
character. The importance of this will depend on whether in
other methods any error is shown due to characteristics of the
compared lights, other than their luminosity.

Measurement of illumination is possible by determining the
critical frequency of flicker. The method is subject to very
much the same criticisms as apply to measurement by visual
acuity. Taking as illustration the investigation of Kennelly
and Whiting, we find that " every time the illumination on
the target is doubled, the mean vanishing flicker frequency
iucreases by 3'3 cycles per second approximately/' The
observations of each observer used to obtain the mean of three
show sometimes values or 2 cycles per second above the
mean adopted, sometimes as much below, indicating a possible
range in settings corresponding to about 100 per cent, in
illumination. In short, the method appears to be not so much
for accurate light measurement as for orders of illumination.
It possesses the characteristic noted in connexion with visual
acuity methods, namely, that it is not necessary to view the two
differently coloured fields simultaneously in order to make a
measurement; two illuminations equal to a third are, therefore,
of necessity equal to each other. Tests of the results of
adding illuminations of different colours are lacking.

A word may be said in passing in regard to the common
characteristic of the last two methods, that by neither is it
necessary to juxtapose the observed illuminated surfaces. In
one way this is an advantage. The problem of judging
between two hues is eliminated. Judgment is made on a
quality common to both illuminations (their detail or flicker
revealing power) which is not confused by hue, as is the
sensation of brightness. On the other hand, both visual acuity
and ability to perceive flicker are largely influenced by physio-
logical conditions such as adaptation and fatigue, and are apt
to vary from time to time. The uncertainties introduced by
these latter are probably as great as the uncertainties of indi-
vidual settings during one measurement. At any rate it is
significant that none who have worked with either visual acuity

156

Mr. H. E. Ives on the

or critical frequency in their relation to illumination have
seriously proposed using them as means of exact photometry.

The last method to be considered is that of flicker
photometry. The flicker photometer owes its applicability
to heterochromatic photometry to the fact that colour fusion
occurs before brightness fusion ; that is, the sensation o£
flicker caused by alternation of one colour with another dis-
appears at slow speeds of alternation, resulting in a field of
uniform hue in which is an outstanding flicker. This out-
standing flicker disappears only when the two illuminations
bear a certain relation to each other. For lights of identical
colour the point of disappearance of flicker corresponds
exactly with the point of equal illumination. With lights
of different colour this point certainly corresponds closely
with equality as measured by other methods, though perhaps
not exactly.

The flicker method has found many advocates because
of its superior definiteness as compared with the method
of direct comparison. The comparison of different hues is
eliminated, apparently by a process which separates luminosity
from hue, leaving a phenomenon — flicker — of considerable
delicacy. Whitman, Rice, and others find settings between
lights of different colours nearly as easy as between lights
of the same colour. The accuracy of setting compares well
with that of direct comparison between lights of the same
colour.

Work by Whitman and Tufts would appear to show that
the flicker method possesses this further requirement of a
method of measurement : that several illuminations acting
together measure to the arithmetic sum of their values
measured alone. In short, the flicker method appears to
yield greater definiteness than the method of equality of
brightness, and to have the same qualifications of a method
of measurement as Abney's work would show for the latter.
Spectral luminosity curves obtained by the flicker photometer
have shown considerable similarity to those by other methods,
so that the special requirements of a method of coloured
light photometry appear to be well met.

From this review it seems that the study of methods of
heterochromatic photometry would most profitably centre
around the equality of brightness and flicker methods. Con-
census of practical opinion agrees with this, for it is with the
different values given by these two methods that photo-
metrists are now largely concerned. From the manner in
which each meets the requirements outlined above, it might
seem as if both are suitable, with the advantage in favour of

Photometry of Lights of Different Colours. 157

the flicker method because of its greater defmiteness. It
might be expected too that the methods would agree. Yet
apparently this last is not the case. The flicker method
has not been so generally used as its convenience would
recommend, because numerous disagreements have been
recorded between its renderings and those of the longer
established method of direct comparison or equality of
brightness. The explanation of these differences is most
likely found in the different conditions which have obtained
when the characteristics of the two methods have been
studied, and when comparisons have been made between
them. The importance of certain physiological conditions
will be emphasized in the next section. The most signi-
ficant facts are that the methods do not in general agree,
and that the tests to which they have been subjected, in par-
ticular by Abney and by Tufts, were under conditions radically
different than those of practical photometry. The most
pressing subject for investigation just now is, therefore, the
relation between these two methods, under various conditions.
What the important conditions are will be made clear by
consideration of certain physiological factors.

Physiological Factors,

The relative sensibility of the eye to different coloured
lights is considerably affected by changes in illumination and
by changes in the size of the field of view. According to
present theory, these differences are due to the irregular
structure of the retina and to the preponderance of different
seeing elements at different illuminations. Two sets of
elements are present in the retina — rods and cones. Ac-
cording to the " Duplicit'ats Theorie " of von Kries, the rods
are chiefly responsible for vision at low intensities, the cones
at high. The cones are sensitive to colour with a maximum
of sensibility in the yellow ; the rods are not sensitive to
colour, but have a maximum of sensibility at a wave-length
corresponding to the green. These elements are distributed
unevenly over the retina. At the centre (the fovea) there
are no rods ; both rods and cones are about equally dis-
tributed in the surrounding central region called the macula
lutea; while in the outer regions of the retina rods pre-
dominate. Hence, either increasing the size of field or
decreasing the illumination brings into play more of the
rods, thereby explaining the Purkinje and yellow-spot
effects.

Whether the rod and cone theory will prove the true

158

Mr. H. E. Ives on the

explanation of retinal action is not at present of great
moment. The facts about retinal structure on which it is
based are, however, to be kept in mind while studying
colour photometry, as indicating the most probable critical
points in the series of changes which may be rung on
conditions.

The complications introduced by colour blindness will not
be a main topic of the present research. The object will be
to secure data from normal eyes, on the understanding that
only observers of normal vision are equipped for photometry
with lights of different colours. The comparison of various
methods with one another, and the investigation of each as
to its qualifications as a method of measurement, can be made
by one observer, and in fact should be so made first of all, as
thereby differences in method are not confused with differ-
ences between observers. Some data obtained by several
observers of normal vision have however been collected with
a view to testing the generality of the phenomena found, and
to determine how much variation exists among observers
with no marked abnormalities of vision.

Adaptation and fatigue are probably the physiological
factors most difficult to estimate and control. Colour vision
is peculiarly dependent on adaptation. When physiologists
work on problems of vision they distinguish between the
light-adapted eye and the dark-adapted eye, depending on
whether the eye works in the light or in comparative
darkness. The ability to perceive colour, which is lost on
greatly decreasing the illumination, gradually returns as the
eye becomes accustomed to the small quantity of light.
Fatiguing the eye for one colour makes it more sensitive to
others. Fatigue also alters the relative critical frequencies
of flicker for different colours ; and the effect is different
depending on the character of the fatiguing light.

Both these disturbing factors must be kept in mind when
investigating heterochromatic photometry, but their detailed
investigation must wait until the more prominent phenomena
have been covered. It is to be noted that the effects ot
adaptation and fatigue are brought out by extreme con-
ditions, such as very high or very low illumination. In
ordinary photometry the eye is probably in the condition
called by physiologists " light adapted," because of the order
of illumination used, and because of the use of auxiliary
lights for such things as scales and data sheets. If obser-
vation has not been too long continued or if the illumination
is not trying, the effects of fatigue may be kept at a minimum.
The policy in the present investigation has been to maintain

Photometry of Lights of Different Colours. 159

the conditions of lighting at nearly those of practical photo-
metry, and, by making observations for only a limited time
each day, to prevent the eye from becoming fatigued to such
an extent as to be noticed by difficulty or discomfort in making
readings.

Summarizing the physiological considerations we find that
an investigation of heterochromatic photometry must include
studies of the effect of varying the size of the photometric
field and of varying the illumination. A complete study will
include observations for a large range of illuminations and
for several sizes of field at each illumination. The state of
adaptation of the eye must be as nearly as possible that
holding under the conditions of measurement to which results
are to be applied.

I.

Spectral Luminosity Curves as obtained by Flicker
and Equality of Brightness Photometers.

Previous comparisons of the two photometers. — The most
extensive comparisons heretofore made between these photo-
meters are those of Dow and Stuhr. Comparisons of less
complete character have been made by Millar, Wilde, and
others. Dow, recognizing the importance of the physio-
logical factors above emphasized, has studied the effects of
change of illumination and of field-size. For this purpose he
used coloured glasses over his light sources. Comparing, for
instance, red and green lights, he found by direct comparison
that on decreasing the illumination the relative brightness of
the red decreased, the decrease being very rapid from *2 metre
candle down. With the flicker method this decrease was
hardly observable, and the change at *2 metre candle was
not shown, although the difficulty of flicker measurements is
too great at low illuminations to establish this difference with
certainty. On decreasing the size of the field, at a fixed
illumination, the brightness of the red increased by equality
of brightness ; by the flicker method a much smaller increase
was found. These experiments were carried out with the
same sized field and the same illumination for each method,
so that on that score the results are beyond criticism. They
indicate that the flicker method is less susceptible to the
influence of changed illumination or size of field.

Stuhr has compared the methods of visual acuity, direct
comparison, critical frequency, and flicker, using coloured
glasses. He found the methods by critical frequency and by
flicker to yield identical results. These differed both from

160

Mr. H. E. Ives on the

the results of visual acuity and equality of brightness mea-
surements, lying between these latter. Different field-sizes
— unspecified — were used for visual acuity and other mea-
surements, and in no case was attention paid to the absolute
illumination. In other words, the physiological factors were
not considered.

P. S. Millar describes measurements of a mercury arc
against incandescent lamps in which the illumination varied
over a wide range. With equality of brightness photometers
the mercury arc measured relatively much brighter at low
illuminations : with flicker photometers this effect was absent.

Wilde describes measurements of a tungsten lamp against
a carbon, made with a flicker photometer and with an
equality of brightness photometer. The photometers showed
a disagreement of several per cent.

Of these comparisons that of Dow is by far the most
complete and scientific, establishing as it does that the two
methods give different results for the same size field when the
illumination is changed, and that at a fixed illumination they
respond differently to changes of field-size. The two points
in which Dotv's work is incomplete hold also for the work of
the other investigators quoted, while their work is less
complete in other ways. First, it is to be noted that the
experiments refer to no definite scale of colour, such, for
instance, as the spectrum. It is therefore impossible to
calculate from his results the magnitude of the effects of
varying conditions for any given energy distribution.
Second, while the effect of varying either illumination or
field-size was investigated, the investigation was not con-
tinued to the point of varying both together. There is, for
instance, a large range of illuminations suitable for the
carrying out of measurements. At each of these illuminations
anyone of several sizes of field maybe used. Our knowledge
of the relative behaviour of the two methods is incomplete
until we know, on some definite colour scale, how these two
variables — illumination and field-size — affect the criteria fur-
nished by the methods, for all practicable combinations of the
variables. The importance of this knowledge may be indicated
by considering the character of the differences between the
methods as indicated by Dow's work : —

The Purkinje effect is less with the flicker method. We
also know from the work of Kcenig and Brodhun that the
Purkinje phenomenon practically disappears for high illu-
minations. The effect of decreasing field-size is (according
to Dow) less for the flicker method, but we also know that
the Purkinje effect by direct comparison has been found

Photometry of Lights of Different Colours. 161

much less for small fields. That is, by using high illuminations
and small fields the differences between the methods are less
than for low illuminations and large fields. At once there
opens the possibility that by proper choice of illumination and
field-size the two methods may agree. Should this be the
case, it would be a strong argument for choosing that illumi-
nation and field-size as the standard one for making colour
comparisons. The possibility thus indicated is sufficient for
undertaking a complete comparison of the methods.

Apparatus and Procedure.

The method of attacking the problem was to determine
by the two methods and under various conditions the lumi-
nosity curves of a spectrum of known energy distribution.
The apparatus used is similar in some respects to that of
Tufts, and is shown in fig. 1. A Hilger constant-deviation

Fig. 1. — Arrangement of Apparatus.

1. Observing slit. 6. White sector-disk. 10. Light source.

2. Prism table. 7. Photometer bench. 11. Photometer bench.

3. Collimator slit. 8. Standard lamp. 12. Diaphragm.

4. Divided drum. 9. Diffusing glass. 13. Diaphragms used.

5. Wave-length drum.

wave-length spectrometer forms a spectrum of the light
source upon an eye-slit (1) of dimensions \ by 2 mm. The
eye placed at this slit observes the prism face (2) illuminated
Phil. Mag. S. 6. Vol. 24. No 139. July 1912. M

162

Mr. H. E. Ives on the

by monochromatic light o£ a purity determined by the
relative size of collimator and eye-slit (3 and 1). The
wave-length incident on the eye-slit is changed by motion
of the drum (5). The size of the collimator slit is changed
by turning the drum (4) which is provided with a divided
head. At (6) is a thin metal disk of the shape shown in
separate sketch. This has carefully bevelled edges and is
painted white. Periodically the disk is smoked over burning
magnesium wire, so that the surface used is of white mag-
nesium oxide. At (7) is a photometer track, carrying a
movable incandescent lamp (8). The disk is connected by a
belt with a direct-current series- wound motor in series with
a variable resistance, and the same belt passes over the
pulley of a Weston electric tachometer. At (9) is a piece
of finely ground glass; at (10) a frosted bulb tungsten lamp,
movable on a photometer track (11). At (12) may be placed
diaphragms of any desired size.

For light source at (10) the requirements to be met were:
first, as high intensity as possible; second, as white a source
as possible, since prismatic dispersion and the selective
absorption of the prism glass both decrease the amount of
blue light for practicable slit-widths. A tungsten lamp
burning at normal voltage was ultimately decided upon. At
frequent intervals this was checked for colour upon a photo-
meter by ascertaining the voltage to give the integral colour
of three standards which were not burned at any other time.
This proved fairly satisfactory, although some change in
distribution undoubtedly occurred during the investigation,
due partly to blackening of the bulb.

For light source at (8) carbon lamps were used, of uniform
colour, ranging in candle-power from 65 to 5. These placed
at. various positions along the photometer bench permitted
variations of illumination from 1 to 600 metre candles. The
colour chosen was that of the incandescent lamp secondary
standards at present in use, namely that of a 4*85 watts
per mean spherical candle treated carbon, oval anchored
filament. Use of an unsaturated colour of a particular hue
will of course give results applying only to comparisons with
such a standard. The complete study of the question will
probably demand investigation of any possible effects of
altering the character of the standard light.

The method of obtaining the luminosity curves is as
follows : — The lamp (8) is placed to give a certain illumi-
nation ; the disk (6) is turned so that the photometric field
is bisected ; the drum (5) is set at a point near the middle of
the spectrum (taken always arbitrarily to give a mean wave-

Photometry of Lights of Different Colours.

163

length of *574/*); the divided head (4) is turned to give a slit-
opening of 10 units (O'l mm.) : the lamp (10) is then moved
until the two halves of the field are, as nearly as can be
estimated, equally bright, at which point the lamp is fixed.
A set of readings is then made, first by equality of brightness,
then, with the disk rotating, by the flicker method, intensities
being matched by changing the width of the slit (3). The
wave-length drum is then changed to a point in the red,
next to a point in the green or blue ; and so alternating from
one side of the original point to the other, similar double sets
are made. When the whole spectrum as far as practicable
is covered, a set of slit-widths is obtained, the reciprocals of
which are as the brightnesses of the colours. By this means
the illumination is constant throughout any one measurement
— an important condition, which has been overlooked by
several investigators.

Three sizes of field are used : one corresponding to the
whole prism-face, an oblong 18 X 24 mm., somewhat larger,
as viewed at 20 cm., than the angle subtended by the macula
lutea; the second, a circular opening of 16 mm. diameter,
subtending at a distance of 20 cm. an angle a little less than
the macula lutea ; the third, a circular opening of 6*5 mm.
diameter, corresponding to the angular size of the fovea. At
each illumination a set of equality of brightness and flicker
measurements is made for each field-size. The making of
such a set for one field-size consumes a morning or afternoon,
and but one can be made safely in a day without unduly
fatiguing the observer.

The measurements so obtained are subject to several
corrections. These are : first, that for slit-width ; second,
that for prismatic dispersion ; third, for the selective absorption
of the prism ; fourth, for the energy distribution of the source
whose spectrum is used. The illumination as measured by the
intensity and distance of the lamp (8) must be corrected for
the loss by absorption through the telescope lens.

To determine the slit-width correction it is necessary to
know the approximate luminosity curve and the portion of
the spectrum included in each measurement. The latter was
determined for the whole range of slit-widths used, and for
the largest slit was found to amount to '03 fi at "66 /u,, and to
•01 fju at *49 fx. In the yellow, where the luminosity curve
changes its direction most rapidly, the greatest width used is
*016 /jl. In this region the correction calculated from the
approximate luminosity curves is 0*6 of one per cent. This,
the largest correction, is of the order of magnitude of the
errors of observation, and may therefore be neglected.

M2

164

Mr. H. E. Ives on the

The correction for prismatic dispersion was determined by
measurements of the wave-length interval corresponding to
the width of the eye-slit, using the drum divisions and spectral
lines of known wave-length.

The correction for prism absorption and for energy distri-
bution were determined together. Spectrophotometry com-
parison was made between the light of an incandescent lamp
previously compared with a black body of known temperature,
and the light of the tungsten lamp source through the ground
glass (3) and the prism (2). Employing the Wien equation

14500

Jk = c{\. e at to determine the energy distribution for the
black body at the temperature measured, the distribution
of energy from the source as used is given in fig. 11
(PL III.).

The calculated illuminations due to the various lamps placed
on the photometric bench (7) are subject to a reduction of
10*5 per cent, as determined by measuring the absorption
of the telescope lenses in a photometer.

A large number of observations of the character described
were made almost daily during a period of about six months
by the writer, and by other observers as will be noted.
Illuminations were used whose corrected values are 1'8, 2*9,
8'9, 16*1, 26-9, 33, 68, 110, 175, 270 metre candles. These
illuminations, because of the artificial pupillary aperture of
1 sq. mm., correspond to lower illuminations in practical
photometry ; they will therefore be referred to here as
" illumination units."

The observations were plotted on thin, rather transparent
coordinate paper, which permitted each observation to be
compared with any other by simply superposing and holding
to the light. This plan suited admirably; for in order to
make all the comparisons necessary, each curve had to be
studied in several different combinations. The same plan
is of course impossible in publication, so that it will be
necessary to select certain representative curves and to plot
several in each diagram ; the same curves will for that reason
figure several times. The necessity for this will be evident
from the following list of the combinations necessary for a
complete comparison with one observer alone.

(1) Effect of changing illumination, for each of three field-sizes.

(a) On the direct comparison curves.

(b) On the flicker curves.

(c) Relative position of the two curves due to the

change.

Photometry of Lights of Different Colours. 165

(2) Effect of changing size of field, at each of ten illuminations.

(a) On the direct comparison curves.

(b) On the flicker curve.

(c) The relative position o£ the two curves due to the

change.

Among the curves are some showing bad points and some
which, as the text indicates, do not exactly agree with those
taken at other times. These imperfect curves (practically all
" equality of brightness 33 curves) are used because even with
their defects they show a proper relation to the preceding and
following ones, while curves made at a later date purposely
to replace them would correspond to a changed criterion.
Attention must be called to the fact that in the measurements
involving physiological variables, it is impossible to exactly
reproduce conditions holding at one time ; hence data must
occasionally be used for which, were it possible, one would
by preference substitute other determinations. The curves
selected have been most carefully chosen so as to represent
most clearly the various phenomena brought out by the
measurements.

Every effect to which attention is called and every con-
clusion is supported not only by the curves shown in this
article, but also by others made at intermediate illuminations.
Further, to avoid any possibility of error due to change in
the light source between measurements, check settings at one
time have been made to verify (at least qualitatively) those
phenomena which are indicated by the differences between
curves made on various days.

The data here presented consist principally of three sets :— -

1st. Measurements made by the writer, chiefly during a
period of about eight weeks in May, June, and
July, 1910.

2nd. Measurements made by Mr. Luckiesh during July
and August.

3rd. Measurements made at selected points for one field-
size by five observers of normal colour vision during
two weeks in September.

These will now be considered from various points of view.
In turn will be taken up :

(a) Relative sensibility of the flicker and equality of

brightness methods.
(5) Reproducibility of measurements,
(c) Effect of changing illumination on each method for

each field-size.

166

Mr. H. E. Ives on the

(d) Effect of changing field-size on each method, for
various illuminations.

(e) The relative positions of the luminosity curves by
the two methods at various illuminations and field-
sizes.

(/) Comparison of luminosity curves obtained by dif-
ferent observers.

{a) Sensibility.

A measure of the relative sensibility of the two methods is
obtained by taking the mean error of setting. In fig. 2
(PI. III.) are plotted the mean errors for five observers at
250 illumination units for various points in the spectrum,
from the deep red at '66 fi to the green at '51 /jl. The mean
flicker errors are given by the full line, the mean equality
of brightness errors by the dashed line. In fig. 3 are
given the same quantities as obtained from observations at
10 illumination units. Several facts are here brought out
clearly. First, the flicker method is for all parts of the
spectrum several times as sensitive as the equality of bright-
ness method at the higher illumination, the relative sensibility
differing for different observers, but always favouring the
flicker method. Second, the difference in sensibility between
the methods is greater at high illuminations than at low. At
the lower illumination the equality of brightness sensibility
becomes greater, the flicker sensibility less. Third, the sensi-
bility by the flicker method is less toward the ends of the
spectrum, where the difference in hue between the spectrum
colour and the standard lamp colour is greatest.

It is to be noted that while all five observers made readings
by the flicker method which compared very closely to the
accuracy of those made by the two most experienced obser-
vers (H.E.I, and M.L.) two of the others (by wliom settings
were made for the first time) averaged five or ten times the
error by the equality of brightness method as by the other.
This illustrates the great superiority of the flicker method as
a method of measurement with observers not used to making
matches between lights of widely different colour.

In connexion with the question of sensibility may be given
the data on the speeds used with the flicker photometer. As
is well known, sensibility varies with the speed, being less
at high speeds. In fact, with high enough speed all flicker
vanishes, no matter what the difference in illumination from
the two sources under comparison. In these experiments the
speed was always adjusted to the lowest value at which
flicker could be made to disappear. This was then read by

Photometry of Lights of Different Colours. 167

the tachometer and reduced to cycles per second. In fig. 4
(PI. III.) are given the speeds as used by the different ob-
servers from end to end of the spectrum and for the two
illuminations. The data show that much lower speed is
necessary for low illumination, and that the ends of the
spectrum require higher speed than the middle. These facts
readily fit in with our knowledge derived from other sources
and with such theory as we have of the action of the flicker
photometer. The eye is more sensitive to flicker at high
illumination than at low, hence the greater sensitiveness of
the flicker method and the higher speed necessary at high
illuminations. In order to compare lights of different colours
it is necessary to attain such a speed that the colour flicker,
due to difference in hue, disappears. It is therefore to be
expected that at the ends of the spectrum where the hue is
most different from the comparison lamp, a higher speed is
necessary, and with this higher speed goes decreased
sensibility. Whether the change in sensibility is exactly
what the change in speed would occasion, or whether the
change in speed is conditioned by hue difference alone, are
points for future study.

In fig. 5 (PL III.) are plotted some preliminary data upon
flicker speeds and sensibility under varied conditions of field-
size and direction of vision. The two upper curves show the
speeds (at 270 illumination units) for the largest and smallest
fields used. The large field requires the higher speeds ; in
other words, it is more sensitive to flicker. The lowest curve
gives the speeds used for observation by peripheral or averted
vision. To obtain these the smallest aperture was displaced
to one end of the total available opening, and attention was
fixed upon a small pin-hole (in which no flicker was visible)
at the other end, about 8° distance, flicker being observed
at the small aperture. The most striking feature is the
much lower speed, corresponding to that required for lower
illumination. Above are plotted the mean errors for
observation by peripheral vision. These are much larger
than by central vision. Later, the theoretical bearing of
these points will be discussed. It is hoped ultimately to
follow them up with more extended investigations of the
retinal field, not only for speed and sensibility, but also for
the character of the luminosity curves. These have,, however,
been deferred until some of the points of more direct interest
to photometry are studied, although the complete explanation
of the phenomena encountered will probably be brought out
by study of extreme conditions, snch as those holding in
peripheral vision.

168

Mr. H. E. Ives on the

(b) Reproducibility of Measurements.

Early in the course of the investigation a brief test of the
reproducibility of measurements was made. It was then
found that measurements made from day to day agreed to
within the errors of measurement ; that is, the individual
flicker points agreed to within one to five per cent, depending
on the part of the spectrum, while the equality of brightness
points agreed somewhat less well. The chief object of the
investigation at that time being to obtain knowledge of the
relative positions of the two kinds of luminosity curves as
simultaneously obtained, no further study of the question
of reproducibility was made until the great body of curves
here plotted were obtained.

At the conclusion of the measurements by the second
observer (M.L.) the writer made a number of check measure-
ments, which established a fact that had before been indicated
by other occasional measurements, and by the measurements
of M.L. This is that the equality of brightness curve may
change its position with respect to the flicker curve in course
of time. It appears that one's idea or criterion of a match
in intensity by equality of brightness may change as com-
pared with the flicker criterion, assuming the latter to remain
fixed. Thus in the set of measurements given in Plate I.
(PL IV.) the equality of brightness method showed, for large
fields, the red less bright in proportion to the blue than did
the flicker method. Three months later, after an interval
of other work, the writer obtained, under the same conditions
as before, curves with the red brighter by the equality of
brightness method than by the flicker method ; in other
words, the equality of brightness curve had shifted from
one side to the other of the flicker curve. The first curves
of Plate I. and Plate v. (made on different lamps) show this
change of relative position just described.

As to the amount of change experienced by each curve,
the data as obtained do not give as complete an answer
as is desirable, because some changes in the distribution of
energy in the tungsten lamp took place in the interval
of time, due to blackening, etc.; and in the last measure-
ments an entirely new lamp had to be used. As the curves
stand, they show slight changes in the flicker points, but
very large in the equality of brightness ones. Taking
into account the changes and differences in the lamps, it
appears extremely probable that the flicker luminosity curve
remains fixed to within the errors of measurement, while the
equality of brightness curve remains fixed to within the errors

Photometry of Lights of Different Colours. 169

of measurement only so long as one's memory retains the idea
first formed as to the brightness of coloured fields. In course of
time the latter curve may experience changes much greater
than the change given by the errors of measurement.

A satisfactory test of reproducibility can only be made
with lamps and apparatus standing absolutely unchanged
between measurements — a condition which cannot be abso-
lutely maintained. Nevertheless, a test approaching this in
character has been carried out since the conclusion of the
comparative measurements by different observers. Two
seasoned " 4-watt " carbon lamps have been used as sources,
the apparatus has been clamped rigidly in position, and at
intervals of about a week, for a period of two months, flicker
and equality of brightness curves have been made by two
observers. The middle-sized field was used, at the highest
illumination (270 units).

In fig. 6 (PI. III.) are plotted the mean deviations from the
mean, or the mean error of setting, where the mean of all is
taken as correct. These show less satisfactory reproducibility
by the equality of brightness method than by the flicker method.
The difference is not everywhere, however, as great as might
be expected from the relative sensibility data and the con-
siderations above mentioned. It must, however, be borne in
mind that these results are obtained by two very practised
observers, whose criterion of equality of brightness had
become well fixed long before those measurements were
made. With new observers or with observers who rarely
made comparisons involving such large colour differences,
the equality of brightness method would not have shown up
so well. The indications are that with practice one's criterion
becomes apparently fixed so that equality of brightness com-
parisons can be made with a high degree of reproducibility,
though not with as high a degree as the flicker method.
Whether this criterion is correct or not is another matter.

A point which deserves mention is the question of repro-
ducibility at low illuminations. There it has been found by
experience that reproducibility is much less satisfactory by
both methods, and for a pretty clear reason, viz. one's illumi-
nation scale at low illumination is not a fixed but a shifting
thing, due probably to the different physiological condition
of the observer at different times. A set of curves for three
field-sizes, for instance, will be obtained on three successive
days and will show a certain relation at a given low illumi-
nation. After an interval of several days or any interruption
of habits, an attempt to check these may give three curves
consistent with themselves but corresponding either to a

170

Mr. H. E. Ives on the

higher or lower illumination than the earlier curves. It is
thus out of the question to ascribe a certain luminosity curve
to a definite illumination, since the same illumination in
metre candles corresponds at different times to different
retinal conditions. Where then in the appended curves the
illuminations are given for the low illumination observations,
the figures indicate under what conditions the measurements
were made, but do not necessarily mean that any one curve
is only to be obtained at just that number of metre candles.
The order of illumination is the important thing here, and
the trend of the phenomena with changing illumination.

Work on the border-line between physiology and physics
tends to shake one's faith in the principle of universal causa-
tion. Faith may be reconciled with experience only by
constant reminder that however exactly physical conditions
may be reproduced, one's physiological apparatus of seeing
cannot be brought to a previous condition by any amount of
careful work with metre stick or voltmeter.

These remarks on the shift of one's illumination scale
apply only to illuminations of the order of twenty units and
below ; above that figure this difficulty disappears, and for
that reason the reproducibility test described above was made
at high illumination. Needless to say, the difficulties of low
illumination measurements have necessitated close applica-
tion and considerable repetition of work in order to secure
the data presented.

(c) Effect of changing illumination, on each method,
for each field-size.

In Plates I. and i.a (PI. IV.) are given luminosity curves as
obtained by the two observers by whom the complete sets of
measurements (illumination and field-size varied) were made.
These as plotted are corrected for prismatic dispersion, but not
for the energy distribution of the source, and are arbitrarily
made equal at '574 /jl. In the upper row are shown the
curves obtained by the flicker method, four different illumi-
nations being plotted together, in three groups, each repre-
senting one size of field. In the lower row the same data
are given for the equality of brightness method. Appended
keys indicate the illumination and field sizes in question.

From these curves it appears that the effect of change of
illumination is to shift the luminosity curves along the
spectrum. The most striking phenomenon is that while
the shift with the equality of brightness method is toward
the blue (Purkinje effect), the shift with the flicker method is

Photometry of Lights of Different Colours. 171

toward the red, or exactly opposite. Also to be noted is
that with the smallest field these shifts are less marked.

Examining the curves more in detail, several interesting-
points appear. Taking first Plate I. (H.E.I.) and examining
the quality of brightness (lower) curves, it appears that the
effect of decreasing illumination is two-fold : first occurs a
broadening of the curves (increase of area), then an increase
on the blue side, which results in a shift of the whole curve
toward the blue. This may be interpreted as an increase on
the red side, followed by an increase on the blue side, the
latter becoming more marked at lower illuminations. With
decrease in the size of the aperture these changes are much
less, which is in accordance with the oft encountered
statement that the Purkinje effect is absent for very small
fields.

The flicker curves exhibit a plain shift toward the red,
with not much difference for the different field-sizes until
the lowest illumination is reached. At this lowest illumina-
tion there appears a drop on the red side, most marked for
the largest field-size. In consequence of this the area of
the curve is less and its maximum shifts again toward the
blue.

Consulting Plate I. a we find the same general phenomena
exhibited, a shift toward the blue for equality of brightness,
toward the red for flicker, with decrease in illumination.
Some differences between the results of the two observers
are to be noted. Chief among these is that the correspond-
ing changes in the curves take place at different illumina-
tions and field-sizes from those of the first observer. The
lowest measurement, for instance, was made at an illumi-
nation where the writer could secure no reliable flicker
measurements.

As to the equality of brightness measurements, it is to be
noted that the increase of luminosity on the red side of the
curve is absent with the large aperture, slight with the middle
aperture, and pronounced with the smallest aperture. The
smaller increase of the blue sensitiveness or Purkinje effect
with the small field is not only present, but because of the
enhanced red sensitiveness the maximum of sensibility for
low illuminations actually shifts toward the red, somewhat
as the flicker curve for the same field-size and illumination.
As a consequence of these facts the curves of this plate do
not show a broadening of the curves, preceding the shift
toward blue. The small aperture lowest-illumination curve
seems to indicate a drop in red sensitiveness, or a reversal
similar to the one occurring with the large field flicker curves

172

Mr. H. E. Ives on the

with the writer. These secondary effects occur at the lowest
illumination, where measurements are difficult, and thus
cannot be established so well as the high illumination
phenomena.

The flicker curves show similarly different effects due to
changed illumination at different field-sizes, for while all
show an increase of red sensitiveness for low illumination,
the effect is most marked with the large field. There is no
apparent reversal of the direction of the shift, although at
the lowest illumination there is an increase of blue sensitive-
ness accompanying the increase of red, with the largest
aperture. This is on a parallel with the drop in red sensi-
tiveness at low illumination for large field in the writer's
case.

One point is not well shown on these curves (which were
selected to illustrate extreme cases), viz., that the shifts
plotted occur chiefly at low illuminations. The high illumi-
nation curve represents very closely the position of the curves
for a large range of illumination. Comparative fixity is
found, in fact, from about 70 I.U. up.

The highest illumination (270 units) was the highest it
was practicable to work at with the tungsten lamp. Some
measurements made at about twice this illumination by
viewing an acetylene flame directly showed that no appre-
ciable change in the curves took place beyond this point.

(d) Effect of changing field-size.

Plates II. and II. a (PL IV.) present the luminosity curves at
each illumination, as obtained with each size of field. The chief
facts are, first, that at the high illuminations change of field-
size has practically no effect on the flicker curves. Second,
decreasing the size of field increases the red sensitiveness of
the equality of brightness method (at practically all illumi-
nations) but decreases the red sensitiveness by the flicker
method. In other words, just as there is a reversed Purkinje
effect, with the flicker method, so there is a reversed " yellow
spot effect." In the case of this effect, as with the changes
due to changed illumination, it was necessary for the second
observer (Plate II. a) in order to experience these changes,
to go to lower illuminations than did the first observer.

It is questionable whether the changes plotted in the high
illumination curves for the equality of brightness methods
are true " yellow spot effect " changes, or are due to the
uncertainty of the method. Some check curves made two
months after the first of Plate n., while exhibiting the same

Photometry of Lights of Different Colours. 173

fixed character of the flicker curves, gave the equality o£
brightness curves as substantially the same for all field-sizes.
Triers is, therefore, good ground for believing that at the
highest illumination here used the effects o£ changing field-
size are small or absent by both methods, although the in-
herent uncertainty of the equality of brightness method may
indicate changes even at high illuminations. At lower illu-
minations the changes are of an entirely different order of
magnitude from the uncertainties of judgment, and so can
be described positively. It appears then that the Purkinje
and yellow spot effects are two phases of the same low
illumination phenomenon. In brief, at low illuminations for
large fields there occurs the Purkinje effect by the equality
of brightness method ; the reversal effect by the flicker. At
these illuminations a decrease in the size of the field decreases
the effects.

(e) Relative positions of flicker and equality of
brightness curves.

Plates in. and in. a (PI. V.) give the relative positions of the
two kinds of curves for three field-sizes and four illuminations.
The most striking phenomenon is the large difference in the
curves at low illuminations. At high illuminations the curves
approach each other. In the case of the first observer,
practical coincidence of the two curves is obtained for the
middle-sized field at the highest illumination. In the case
of the second observer (Plate III. a) this coincidence does
not occur, the curves merely being much nearer together
and (as test measurements at higher illuminations showed)
they have reached a " steady state. " With regard to the
different relative behaviour of the two curves with the two
observers, the remarks made on "reproducibility" and the
comparative results of five observers given below, are a propos.
With both the observers whose curves have so far been shown,
there has occurred during the progress of the work a change
of criterion with the equality of brightness measurements,
and in the case of the five observers some show the equality
of brightness maximum to one side, some to the other of the
flicker. The only conclusions that can be drawn are that
the two curves change from wide disagreement at low illumi-
nations to a much closer agreement (in position of maximum)
at high illuminations — the closeness of the agreement being
difficult to determine because of the uncertainty in the real
position of the equality of brightness curves. One point of
significance is that although with both observers the two

174

Mr. H. E. Ives on the

curves have reversed their relative positions on the red side,
and in the comparative measurements by several observers
the curves are differently placed on the red side, it has never
happened that the flicker curve has shown more blue or
green sensitiveness than the equality of brightness. In the
writer's case, the two curves have been obtained exactly
alike within the errors of measurement on two occasions, at
two different high illuminations, with the middle-sized field,
but this is as near as the blue part of the flicker curve has
ever come to crossing over the other. Whether this would
always be the case can only be determined by numerous
measurements either extended over long intervals or by
numerous observers.

It is possible that this phenomenon of lower green sensi-
tiveness by the flicker method may be intimately connected
with the fact that the comparison colour throughout was a
yellowish white. Certain experiments not yet completed
seem to indicate a dependence of the shape of the
luminosity curve by equality of brightness on the colour
of the comparison lamp. It has been found, for instance,
that under certain conditions a spectrum yellow and a spectrum
green may each appear by equality of brightness of the same
intensity as a spectrum red, yet not appear equally bright
when compared directly with each other. One might think,
therefore, that a three-part field could be constructed in
which two colours each appeared equally bright with the
third, at their edges of contact with it, but not equally
bright to each other at their common edge of contact. These
phenomena of simultaneous contrast are yet to be investi-
gated in connexion with the equality of brightness method,
and the question must be settled as to whether any similar
effects occur with the flicker photometer.

Perhaps the most interesting feature in these curves is
their area. Casual inspection reveals the fact that the areas
of the flicker and equality of brightness curves are frequently
not the same. Now if the total light is the sum of the parts,
this would mean the total light greater with one photometer
than with the other. If the spectrum measured were that
of a " 4-watt" lamp exactly like that used as a standard of
intensity, it would be possible to recombine the dispersed
spectrum and make a homochromatic comparison of the two
intensities of standard lamp and measured spectrum. This
would of course be the same by both photometers. In other
words, the physical summation must measure in this case
the same, but by our curves the arithmetical summation is
different by the two methods. One method or the other,

Photometry of Lights of Different Colours. 175

perhaps both, must be deficient as judged by the ability to
add or integrate the measured quantities. This question is
being investigated further.

(£) Comparative results obtained by different observers.

When these measurements were finished it was thought
well to obtain some measurements by other observers in
order to serve as a check, and also to obtain data on dif-
ferences to be expected between observers. Five observers
in all were available, and these are indicated by initials.
H.E.I, and M.L. are the two having previous experience
with the apparatus ; P.W.C., no previous experience with
apparatus, some experience in photometry, considerable ex-
perience in observing with various optical instruments ;
F.E.G., long experience in photometry ; C.F.L., considerable
experience with optical instruments and some in photometry.
These observers have all perfectly normal colour vision.
Before these measurements each observer made a number of
settings with a three-colour mixing instrument (Ives' colori-
meter) to match white. From these settings it appears tbat
the observers differed from the mean by no more than 5 per
cent, in the proportions ol red, green, and blue necessary to
make the match. Differences of this amount are found by
the writer to be the rule with all who fall in the class of
" normal vision." Those occasional observers who would be
classed as partly colour blind will differ by forty or fifty
per cent, from the writer or from the mean of several
" normal observers."

Two illuminations were determined on, a high one of 250
units, a low one of 10 units, and the middle size of field was
used. This choice of illumination and field-size was made
in view of the previous work. The high illumination is one
beyond which no changes in the relative positions of the
curves are to be expected, the low illumination one at which
flicker measurements are still easy to make. The middle
size of field was chosen partly because it is the easiest one at
which to make observations, and partly because the nearest
coincidence of the two kinds of curves had been obtained for
this size.

The apparatus was left undisturbed between experiments.
Except in the case of the observers H.E.I, and M.L., the
divided head on the slit was read by an assistant. The
tungsten lamp was a new one which was given a short
seasoning, and at the conclusion of the measurements its
energy distribution was immediately measured, as before
described.

176

Mr. H. E. Ives on the

Plate IV. (PL V.) exhibits the effects of changing illumina-
tion for the two methods, for each observer, with the mean
curve of all. The chief phenomena of the previous measure-
ments are here borne out. With the flicker method, decreased
illumination increases the red luminosity ; with the equality
of brightness method the same change increases the blue
luminosity (observer M.L. at this illumination shows merely a
broadening of the curve). In the case of the less experienced
observers the equality of brightness measurements are more
or less wild, the flicker measurements very good.

Plate v. exhibits the relative positions of the two kinds of
curves for each observer, with the mean. At the low illumi-
nation the equality of brightness curves are all higher on the
blue side than are the flicker. At the high illumination two
observers place the flicker maximum on the red side, two on
the blue side of the equality of brightness maximum ; one
observer places the maxima about together, although, as has
before been noted, the curves do not actually coincide, being
of different areas.

The mean high illumination curves obtained by the two
methods show close agreement in the position of the maxima;
and it is not unreasonable to expect that with more observers
or more observations extended over such an interval that the
observers would not remember their previous equality of
brightness criteria, the two mean curves would show practical
agreement as to shape and position of maxima. On the other
hand, it is apparent that an exact coincidence of the curves
may not confidently be expected, but rather two curves of
the same shape of slightly different areas.

Figs. 7, 8, 9, and 10 (PL III.) give the luminosity curves
of all observers plotted together. It is obvious from these
that even with workers of normal colour vision considerable
differences may be expected (of the order of five to fifteen per
cent.) in their measurement of pure colours against an un-
saturated colour such as the light of an incandescent lamp.
The observers maintain substantially the same relative posi-
tions with respect to each other, so that the different positions
of their luminosity curves probably represent real differences
in colour vision. The flicker curves lie closer together than
the equality of brightness, so that in general the observers
will differ less on their flicker measurements than on the
others.

It is clear, however, from these curves that whichever
method of measurement is employed, we cannot expect to
obtain results in exact agreement from observers taken at
random, where lights of different colour are to be compared.

Photometry of Lights of Different Colours. Ill

The disagreement between observers will be less in comparing
the unsaturated colours o£ any acceptable illuminants than in
measuring bright spectral colours, but it is nevertheless
evident that in establishing standards of different coloured
lights, either the mean of a number of observers of 44 normal
colour vision" must be taken, or the luminosity curve of
each observer must be known in order that corrections may
be made to his readings — when it is learned how to apply
such corrections.

Fig. 11 shows the distribution of energy in the source used
in the comparative measurements* (tungsten lamp through
prism, &c.) and the mean flicker curve of five observers at
250 I.U. reduced to an equal energy distribution. Since the
flicker curve closely agrees in shape with the equality of
brightness curve, but is more definitely determined, it may
be taken as the mean luminosity curve of these observers,
and probably lies closer to being the luminosity curve of the
normal or average eye than any heretofore obtained. Its
maximum lies at '515 fi. This is in very good agreement
with the high illumination curve obtained by Koenig for his
own eyef.

Summary of results.

The chief new experimental results of this investigation
are : —

1. The flicker method is more sensitive than the equality

of brightness method, where different coloured lights
are compared.

2. The results by the flicker method are more reproducible

than those by the equality of brightness.

3. Decrease of illumination shifts the maximum of lumi-

nosity toward the blue, by equality of brightness
(Purkinje effect) ; toward the red by the flicker
method.

4. Decrease of the size of the photometric fields at low

illuminations shifts the maximum of luminosity toward
the red for the equality of brightness method (yellow
spot effect) ; toward the blue for the flicker method.

5. The relative positions of the two kinds of spectral

luminosity curves are in general different.

* The distribution of energy in the source used for Plates I. and it.
(PI. IV.) for an older tungsten lamp is slightly different from the lamp
used in the comparative measurements.

t The value of '665 /x for the maximum as obtained by Nutting for
Koenig's observations left out of account the correction for the dispersion
of the prism.

178

Mr. H. E. Ives on the

6. The curves are most different in position at low illumi-

nations with large fields ; nearest together at high
illuminations and with small fields. They may under
certain conditions coincide, and the mean curves o£
several observers show close agreement in position
of maxima and shape of the two curves at high
illuminations, although the areas are not the same.

7. The curves obtained by different observers show different

positions for each curve, and different relative positions
of the two for hi oh illuminations. At low illumina-
tions all observers agree in showing the Purkinje and
reversed Purkinje effects above described.

Theoretical Considerations*

No satisfactory theory of the action of the flicker photo-
meter can be said to exist. What does it actually measure ?
We may assume the existence of a " luminosity sense " dis-
tinct from the colour sense. We may then form a geome-
trical picture of the alternations of luminosity as occurring
in one plane, those of hue in another. In the second plane
the sensations fase more quickly, so that the sensation of
flicker due to difference of luminosity persists longer than
that due to difference in hue. Certain experiments by Tufts
on the fatigued eye give some warrant for the assumption of
this luminosity sense. The occurrence of colourless after
images from coloured stimuli may also support this concep-
tion. The luminosity sense may be identified with the black-
white element of Bering's theory. But at present it is
questionable whether this luminosity sense can be considered
as much more than a name used to assist in picturing the
action of the flicker photometer. If it should be established
that there does exist a separate " luminosity " element, which
could be separated from hue by some photometric method,
it would still remain to be established that this corresponded
to our ordinary idea of brightness. If, for instance, there
exists a physiological process called into action both by
coloured and uncoloured light, a measure of this would be a
measure of a common property. This might be satisfactorily
termed " brightness"" by a physiologist, but might not satisfy
the photometrist who is interested not so much in the ultimate
analysis as in things as they appear.

Dow has given reasons for believing the action of the
flicker photometer to be chiefly ascribable to the retinal
cones. The rods are known to be more sluggish, to possess
greater inertia, so that they are less sensitive to flicker. The
fact that the flicker photometer cannot be used at low illumi-
nations, and that, as Dow found, the yellow spot and Purkinje

Photometry of Lights of Different Colours, 179

effects are Jess by it, would support such a belief. The
existence of a reversed Purkinje effect and a reversed yellow-
spot effect, as found in the present investigation, appear to
render Dow's theory inadequate. While a shift from cone
to rod action explains very well the known facts of the
Purkinje and yellow-spot effects and fits with the distribu-
tion of rods and cones in the retina, the flicker phenomena
would appear to call for a more complicated mechanism of
seeing.

Up to the present, the various facts upon which a more
complete hypothesis may be formed are : — 1st, The large in-
crease in blue sensitiveness at low illuminations for large
fields, and the smaller increase for small fields, by the equality
of brightness method. 2nd, The large increase of red sensi-
tiveness at low illuminations for large fields, and the smaller
increase for small fields, by the flicker method. 3rd, The
greater sensitiveness of the flicker method at high than at
low illuminations, and for central as compared with peri-
pheral vision. 4th, The complete failure of the flicker method
at very low illuminations. 5th, The higher speed necessary
for a large field centrally viewed as compared with a small
field, and as compared with a small peripheral field.

Certain of these facts seem to support Dow's contention
that the cones are probably the chief seat of action with the
flicker photometer. The failure of the flicker method at
low illuminations, where the rods are coming into play,
speaks particularly for this. But it is necessary to ascribe
some complexity of structure and behaviour to the cones if
they are to suffice. As has been established by study of the
retina, the cones are scarcer towards the periphery, but at
the same time change in character, becoming larger. If we
ascribe to these peripheral cones the property of exhibiting
the typical cone characteristics (red sensitiveness and sensi-
bility to flicker) more decidedly as the illumination decreases,
we can account for some of the phenomena described above.
In equality of brightness measurements such greater red
sensitiveness in the cones would tend to compensate for the
increasing activity of the rods and to preserve conditions of
vision constant. If the flicker method uses only the cones,
decreased illumination would bring out this compensating
action at illuminations where the equality of brightness
method would show comparatively little Purkinje effect, both
retinal elements still being in action. As a matter of fact the
curves of Plate iv. (PI. V.) for five observers at an illumi-
nation of 10 units do exhibit, on the whole, a more marked
shift toward red by the flicker method than is the shift toward

180

Mr. H. E. Ives on the

blue by the other method. To explain the low sensibility
and low critical speed for peripheral vision — an apparent
reversal o£ the effect caused by increasing the size of the
field — it is only necessary to assume the cones to be present
in too small number, as the distance from the centre of the
field becomes increasingly large, to play an important part.
We then obtain rod flicker, which is produced by low speeds
of alternation.

Along some such lines as this it is possible that the pheno-
mena of the flicker photometer may ultimately receive
explanation. The present work has not been carried suffi-
ciently far into extreme conditions of illumination and
localization upon the retina to establish that the action of
the flicker photometer is to be ascribed chiefly to the cones,
although this may appear probable. Even were this estab-
lished there would still remain the larger part of the problem.
For how do the cones fuse the colour impressions previous
to fusing the " luminosity impressions? Were the facts
exactly opposite, if intensity flicker disappeared first with
increased speed and colour flicker persisted, we could ascribe
the luminosity phenomena to the rods or organs of colourless
vision which possess greater inertia, and the colour pheno-
mena to the cones, in accordance with the commonly known
properties of each. Unfortunately, we must depend upon the
cones for both the colour and flicker photometer phenomena;
hence the need for ascribing to them some complexity of
function as suggested above, and the difficulty of compre-
hending how the separation of luminosity and hue takes place.

Morris-Airey has suggested that the differences between
the nicker and equality of brightness photometers may be
ascribed to the different rates of the rise of sensation with
different colours, a phenomenon which could affect the nicker
but not the other instrument. For instance, in the flicker
photometer, when adjusted to show no flicker, if either light
source is obscured, the violently flickering illumination from
the other source gives a decidedly greater impression of
brightness than if the speed is increased until flicker dis-
appears, or if one-half the steady radiation from that source
is viewed. This apparently increased brightness has been
found different for different colours. If this phenomenon is
taking place even in the absence of all flicker, when the
flicker photometer is at its mid-position, then the different
amount of the effect for different colours might cause a
difference in the readings of the photometers.

As yet this theory has not apparently received any thorough
experimental test. It is not established that at the same

Photometry of Lights of Different Colours. 181

illumination the rates of rise of sensation are actually different
for different colours, and phenomena of this sort are extremely
apt to be influenced by the order of the illumination. Nor
is it established whether these phenomena are functions of
speed rather than of the presence of noticeable flicker. In
other words, whether the disappearance of flicker by alter-
nation with another colour does not destroy these effects as
completely as does the disappearance due to higher speed
with the one colour. There is much yet to be investigated
here, and in view of the differences between observers in
their results as to the differences between the two methods,
it is clear that these phenomena of rise of sensation must be
studied with the same eye and apparatus by which are made
the flicker measurements in which they may play a part.

And so it appears that there is no theory of the flicker
photometer sufficiently supported by known phenomena to
be at present satisfactory. The data collected in this inves-
tigation are probably insufficient to throw much light on the
actual processes at work in the retina, and the investigation
up to the present has had for chief object, apart from the
practical photometric information so urgently needed, the
location of landmarks from which to start the more searching
investigations into the nature of the flicker phenomena and
the brightness sensation.

Investigations which are now being carried on, or are
planned with the same apparatus, are expected to furnish
data which will assist in the formation of satisfactory theories.
Prominent among these investigations may be mentioned :
Luminosity curves as given by the method of critical fre-
quency ; the comparison of the physical and arithmetical
summation of measured illuminations; the effect of changing
the hue of the comparison source ; the phenomena of rise of
sensation as they occur in the flicker photometer as used ;
the connexion between hue difference, speed, and sensibility
in the flicker photometer.

Bearing upon Practical Photometry.

The primary object of this investigation is to decide upon
the photometric method and conditions to hold in deter-
mining the candle-power values of lights of different colours.
Until the completion of the work laid down the full specifi-
cation of these conditions cannot be made. There is as yet
no answer to the question — What is the candle-power of a
light in terms of a standard of different colour ? Certain
conclusions may, however, be drawn at the present stage of
the work which will hold no matter what the final answer to

182

Mr. H. E. Ives on the

the main question. One o£ these is that the sensibility and
reproducibility o£ the flicker method are sufficiently greater
than those of the other method to recommend its use in all
cases where colour differences exist and where the question
of absolute intensity values is not of the first importance.
In the determination of distribution curves of a source, for
example, a flicker photometer would be very convenient. A
second conclusion is to be drawn from the comparative data
by several observers of normal vision. From their differences
of reading it is apparent that differences of colour vision will
always be a serious obstacle to uniform results in hetero-
chromatic photometry. The only practicable escape from
this difficulty is to eliminate the need of making such com-
parisons in ordinary photometric practice ; in other words,
aim to make all practical photometry the photometry of lights
of the same colour.

Under these conditions it is^a matter of indifference what
photometer is used, or whether the observer has normal
colour vision. The problem of heterochromatic photometry
hence becomes one for th9 standardizing laboratory, where
secondary coloured standards or coloured glasses will be
prepared for as many practical cases as possible. The search
for a photometric method for coloured lights will in this
work be treated from that standpoint.

Of considerable practical interest is the fact that the flicker
method most nearly agrees with the method of equality of
brightness at high illuminations. Until the problem is
further toward solution it would appear well, whatever
method is chosen, to make all heterochromatic comparisons
at high illuminations. An idea of the order of magnitude of
the illumination here meant may be obtained by noting that
all the marked shifts (Purkinje phenomena, &c.) occur below
70 I.U. This corresponds to about 1/10 that number of
metre candles as viewed by the normal sized pupil, or
approximately, seven metre candles.

Acknowledgement.

The writer takes pleasure in acknowledging his indebted-
ness to Dr. P. W. Cobb, Dr. C. F. Lorenz, and Mr. F. E.
Cady for their kind assistance in making certain of the
measurements here recorded and used; and especially is he
indebted to Mr. Matt Luckiesh, not only for making many
of the readings but for the preparation of the numerous
drawings and the calculation and reduction of results.

Physical Laboratory,
National Electric Lamp Association,
Cleveland, Ohio, December 1910.

Photometry of Lights of Different Colours. 183

Table I. — Data for Plates I., n., and in. (Pis. IV. & V.)

The flicker luminosity curve for the 4^° field is reduced to
the value unity at '574//. at each illumination, and the other
data are given in terms of this. The data are corrected for
dispersion, but not for the energy distribution of the source.

Field 8°-

6x5°-16

Field 4°-58.

Field l°-86.

X.

Flicker.

Eq. of B.

Flicker.

Eq. of B.

Flicker.

Eq. of B.

Illumination 270 Units.

•657 ju

10-5

•565

14-3

14-2

11-5

13-3

13-3

•643

26-9

215

27 0

25-3

25-0

26-8

•632

42 9

38-8

42-3

41-7

420

43-7

•622

58-8

56-2

58-4

57-5

55-3

61-3

•6125

74-0

71-6

73-9

74-7

70-6

77'9

•593

98-4

98-8

96-0

97-8

98-4

97-1

•574

100-5

103-1

100-0

98-6

1000

1000

•555

89 0

96-8

92-1

92-6

911

93-3

•545

£1-9

88-8

81-4

81-7

810

81-7

•535

66-8

74-3

66-0

67-2

66-5

69-3

•526

50-9

590

51-0

510

493

49-8

•517

34-3

361

330

32-7

320

32-4

Illumination 68 Units.

•655 fx

140

17-4

15-2

•654

15-6

18-8

193

•642

304

30-7

29-0

31 i

30-4

34-4

•632

44-6

460

44-1

49-9

45-5

50-5

•622

596

60-3

59-1

65-4

59-6

653

•612

74-7

76-5

735

81-3

73-4

786

•593

98-3

95-2

95-0

1005

93-9

996

•574

99-0

96-8

1000

102-2

1016

100-5

•555

87-8

93-2

89-8

96-3

88-3

91-2

•545

77-0

81-9

80-8

87-5

79-4

817

•535

64-5

706

679

74-7

66-6

69-2

•526

50-0

57'4

522

57-5

509

52-7

•517

33-3

377

35-5

37-4

31-5

320

Illumination 8*9 Units.

•6525 n

21-6

20-4

20-2

19-2

23-0

. 25-3

•642

37-6

34-4

35-4

37-4

37-9

43-8

•632

51-1

47-1

51-9

51-1

53-4

591

•622

711

68-4

65-8

690

68-6

80-1

•612

83-0

79-8

79-7

790

82-4

95-3

•593

101-6

94-5

101-6

101-5

102-8

116-7

•574

94-9

102-2

1000

102-3

106-4

115-2

•555

84-2

103 9

87-9

108-8

93-4

101-1

•545

716

97-4

75-6

98-0

79-3

91-2

•535

58-1

90-3

61-0

88-2

67-0

78-9

•526

44-8

75-6

48-4

705

50-5

59'9

•517

27-7

54-3

30-9

501

31-6

401

•508

311

20-9

284

19-3

22-5

184 Mr. H. E. Ives on the

Table I. (continued).

X.

Field 8°-6x5°-16.

Field 4°-58.

Field l°-86.

Flicker.

Eq. of B.

Flicker.

Eq. of B.

Flicker.

Eq. of B.

Illumination 2*85 Units.

•653 jx

20-2

142

20-9

17-5

22-6

232

•643

311

25-1

33-3

29-2

35-8

35-6

•632

48-5

43-7

48-7

44-9

49-6

48-1

•622

66-0

53-2

67-8

54-8

64-5

65-2

•612

75-4

65-2

80-3

68-9

78-4

77-5

•594

95-1

78-1

95-3

81-5

93-4

950

•574

95-9

85-9

100-0

90-6

95-9

93-7

•555

76-6

89-7

78-2

90-6

78-8

82-0

•545

66-8

86'6

66- 1

83-2

71-3

76-6

•535

54-3

79-5

54-0

75-8

57-5

67-5

•526

39-2

62 0

37-5

61-6

45-9

54-3

•517

27-9

55-6

25-6

44-7

28-0

35-0

•5075

319

26-0

Table la. Data for Plates n.a, and m.a.

The flicker luminosity curve for the 4-J° field is reduced to
the value unity at '574//, at each illumination, and the other
data are given in terms of this. The data are corrected
for dispersion, but not for the energy distribution of the
source.

X.

Field 8°-

6x5-16°.

Field 4°-58.

Field l°-86.

Flicker.

Eq. of B.

Flicker.

j Eq. of B.

Flicker.

Eq. of B.

Illumination 270 Units.

•655 n

140

120

13-4

12-9

13-1

12-7

•643

24-6

24-9

22-8

26-3

24-9

•632

38-5

38-8

413

38-8

41-8

401

•622

52-7

55-0

53-0

50-4

53-7

51-8

•612

68-9

64-8

68-2

62-7

67-5

65-7

•594

88-0

85-2

88-6

902

88-7

92-5

•574

1004

99-2

100-0

100-8

98-5

105-4

•555

93-7

100-1

91-8

98-0

91-1

1001

•545

83-0

87-0

82-7

91-4

81-8

89-1

•535

70-2

801

71-5

80-6

72-5

78-7

•526

52-9

62-9

55-4

65-8

53-5

61-4

•517

38-0

40-2

35-6

42-4

35-4

40-6

Photometry of Lights of Different Colours. 185

Field 8°-6x5°-16.

Field 4°-58.

Field l°-86.

X.

Flicker.

Eq. of B.

Flicker.

Eq. of B.

Flicker.

Eq. of B.

Illumination 8*9 Units.

•653 fx

20-5

12-6

18-9

15-1

177

16-3

•643

352

19-4

32-8

25-9

33-3

30-8

•632

52-6

30-0

48-5

424

44-6

45-8

•622

66-4

42-6

65-8

54-7

59-7

59-2

•612

78-0

60-9

814

66-3

71-4

72-0

•594

97-6

87-2

96-4

901

91-1

970

•574

101-1

92-8

100-0

100-0

98-3

98-9

•555

90-5

97-7

90-6

96-8

91-1

96-3

•545

78-7

900

804

87-1

53-1

83-0

•535

635

79-5

65-7

8P2

66-9

75-6

•526

50-5

68-4

530

65-0

53-1

59-8

•517

33-2

49-3

33-8

43-9

34-9

41-3

Illumination 2*85 Units.

•653^

11-4

j 261

141

21-5

209

•652

28-8

...

•643

20-0

•642

39-5

38-9

27-6

34-1

32-4

•632

58-7

32*8

53-7

37-0

48-3

46-4

•622

69-5

42-8

696

52-7

63-3

620

•612

84-4

56-6

75-8

65-4

76-7

75-8

•594

98-7

82-0

94-7

82-0

97-3

96-7

•574

101-2

89 0

1000

95'3

98-8

101-2

•555

80-3

928

87-7

99-1

89-1

95-7

•545

75-6

85-1

721

88-6

794

89-4

•535

57-5

81-0

63-2

78-5

66-1

75-5

•526

48-0

61-7

509

66-5

52-7

62-2

•517

35-9

53-8

34-8

48-8

35-0

40 0

•5075

40-6

32-5

Illumination 1*25 Units.

•655

669

•653

23-0

14-0

21-6

20-5

•652

26-0

•643

13*9

•642

33-0

24-6

34-4

31-5

•6415

37-2

•6325

21-6

•632

48-2

37-0

53-8

46-8

•6315

57*3

•622

31 i

61-3

48-4

62-8

60-5

•6215

69-4

•612

77-7

39-4

72-2

57-6

75V3

67-9

•594

88-0

61-5

960

74-5

99-9

90-1

•574

838

71-3

1000

88-6

101-7

1070

•555

71-8

77-4

83-1

81-2

88-3

97-8

•545

60-2

78-5

66-3

85-0

77-6

88-0

•535

53-7

73-8

56- 1

83-4

66-2

72-5

•526

44-1

70-9

471

668

48-8

61-3

•517

37-3

54-2

39-4

516

32-4

46-6

•508

42-5

291

•4975

25-5

1

186

Mr. H. E. Ives on the

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Photometry of Lights of Different Colours. 187

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188 Photometry of Lights of Different Colours.

Table III.

Mean Flicker Luminosity Curve for Five Observers.
Reduced to Equal Energy Spectrum.

X.

653

10-6

643

19-5

622

40-2

612

52-8

593

78-7

574

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555

1110

545

1120

535

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767

Partial Bibliography.

Abney, 11 Colour Photometry," Trans. Roy. Soc. Lond. 1886. p. 423;
1888, p. 547.

Dow, Phil. Mag. Aug. 1906, p. 120, " Colour Phenomena in Photo-
metry."

Phil. Mag. Jan. 1910, p. 58, " Physiological Principles underlying

the Flicker Photometer."
Kcenig, A., Gesammelte Abhandlungen :

p. 144, " Ueber den Helligkeitswerth der Spectralfarben bei

verschiedener absoluter Intensitat."
p. 378, " Die Abhangigkeit der Sehscharfe von der Beleuchtungs-

intensitat."

Kennelly and Whiting, " Frequencies of Flicker, &c," Natl. Elec.

Light Assn., 1907 Convention, vol. i. p. 327.
Langley, " Energy and Vision," Amer. Journ. of Science, xxxvi. 1888.
Millar, Trans, of Ilium. Eng. Soc, Nov. 1909, p. 769.
Morris-Airey, Journal of Inst, of Electrical Engineers, Feb. 1910,

p. 177.

Nutting, Bull. Bureau of Standards, vol. v. p. 261.
Rice, Elect. World, Feb. 24, 1910, " Hetero chromatic Photometry."
Rood, Silliman's Journal, (3) xlvi. p. 173, 1893 ; (4) viii. p. 194,
1899.

Stuhr, " Ueber die Bestimmung des Aquivalenzwertes verschieden-

farbiger Lichtquellen." Erlang-en dissertation,
Tufts, Phys. Rev. vol. xxv. Dec. 1907, p. 433, " Spectrophotometry of

Normal and Colour-blind Eyes."
Whitman, Phys. Rev. iii. p. 24l, 1895.

Wilde, " Photometry of Differently Coloured Lights," London
Electrician, July 16, 1909.

IVES.

Phil. Mag. Ser. 6, Vol. 24, PL III.

Phil. Mag. Ser. 6, Vol. 24, PL IV.

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Plate V.— Relative Positions of the Two Kinds of Curves for the Five Observers.

From the Philosophical Magazine for September 1912.

STUDIES IN THE PHOTOMETRY
OF LIGHTS OF DIFFERENT COLOURS.

ii.

SPECIAL LUMINOSITY CURVES BY THE METHOD
OF CRITICAL FREQUENCY.

BY

HERBERT E. IVES.

[ 352 J

Studies in the Photometry of Lights of Different Colours.—
II. Spectral Luminosity Curves by the Method of Critical
Frequency. By Herbert E. Ives.

r|^HE first paper of this series * described spectral
_1_ luminosity curves obtained by the equality of bright-
ness photometer and the flicker photometer. It was found
that these curves change differently in response to variations
in illumination ; the equality of brightness method exhibits
the Purkinje effect, the flicker method an opposite and
hitherto unobserved shift. At high illuminations the distri-
bution of brightness in the spectrum is closely the same by
the two methods, at low illuminations quite different. With
the standard of comparison used — the unsaturated yellow of
a standard carbon incandescent lamp — the two kinds of
luminosity curves are usually of somewhat different areas
at their nearest approach to similarity in shape. The
differences between the two kinds of curves and the changes
in each due to changed illumination are less with small
fields than with large.

The present paper describes certain spectral luminosity
curves obtained with the same apparatus and conditions as
before but by the method of critical frequency (sometimes
called " persistence of vision ") t- These were studied
primarily with the expectation of obtaining some light on
the peculiarities of the flicker method, with which the critical
frequency method is presumably closely allied. Certain
seeming disagreements in the results of other observers
furnished a starting point for the work here described.
Stuhr, for instance, found that the method of critical
frequency gave results identical to those of the flicker
photometer. But Haycraft \ obtained, by c'ritical frequency
measurements on the spectrum, a pronounced Purkinje shift.
Since, according to the writer's experiments, the flicker
photometer gives a reversed Purkinje effect, it would follow
that this identity of the results of the two methods cannot

* Phil. Mag\ July 1912, p. 149.

t For details of each of the four methods of photometry discussed in
these papers — equality of brightness, flicker, critical frequency, and visual
acuity — reference should be made to the first communication.

\ Journ. of Physiology, vol. xxi. pp. 126-146.

Photometry of Lights of Different Colours. 353

hold for all illuminations. Allen * has obtained " persistence
of vision curves " showing a greater sensibility to pure
flicker in the peripheral retina as compared with the fovea
or central retina. On the other hand, the flicker photometer
has been found by the writer to be less sensitive when the
peripheral retina is used.

The present investigation for the most part clears up these
seeming discrepancies. Most of the results of other observers
have been confirmed. Their divergence is shown to be due
to different experimental conditions.

The procedure for obtaining the luminosity curves was
similar to that described in the previous paper. The largest
field (50,2 x 8°*6) was used most of the time, because with
it the Purkinje and similar effects are most marked. First
a set of flicker and of equality of brightness measurements
was made as in the previous work. Then the spectral light
was extinguished and the speed was determined at which
flicker vanished when the rapidly rotating white disk was
illuminated by the comparison lamp alone. The various
spectral regions were then substituted for the comparison
lamp, and the slit widths were determined which would
cause flicker to disappear at the speed found for the com-
parison lamp. With critical frequency settings the mean of
appearing and disappearing flicker was taken. Ten readings
for each illumination were usually made, and between each
set the eye was rested about a minute in the faint light of
the photometer room. In this manner three kinds of
spectral luminosity curves were found at each illumination.
The first measurements were made at two illuminations, a
medium and a low, namely 50 I. U. and 5 I. U. The results
are given in fig. 1, curves B and C. (Later a variation in
the procedure was found preferable as will be noted and the
curves A, B, and C (fig. 1) were made by this more satis-
factory method.)

It appears from these curves that the flicker and the
critical frequency method both show the reversed Purkinje
effect, in contrast to the regular Purkinje shift with the
equality of brightness method. It appears too that the
areas of the three kinds of curves differ.

The occurrence of the reversed Purkinje shift by the
critical frequency method is in apparent contradiction to
the work of Haycraft. It claimed first attention. For
purposes of comparison Haycraft's results are reproduced in

* Phys, Rev. vol. xi. p. 257 ; vol, xxviii, p. 455

354

Mr. H. E. Ives on the

Fig. 1.

A 3oo l u.

o Critical frequency"

• FLICKER

0 SO IU

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Xnverse Luminosity Curves by Critical Frequency, Equality of Brightness,

and Flicker Methods.

fig. 2 *. In his work Haycraft adopts a different procedure
from that of the writer. The illumination is not kept
constant throughout the spectrum, but is taken as it naturally
occurs, consequently the ends are always much darker than

* Haycraft, loc, cit.

Photometry of Liglits of Different Colours. 355

the middle. He plots critical frequencies for constant slit-
width, instead of slit-widths or reciprocal slit-widths for
constant frequency as is here done. It is in this difference

Fig. 2.

«oc «30 4<oO tao ,reo sso seo t>so 6va 6?o 7oo 730 7*0

Critical Frequencies of the spectral colours at high, medium, and low-
intensities, showing- relatively greater change for red (R). After
Haycraft.

of procedure that we find the explanation of the difference
between Hay craft's results and those of the present writer.
An examination of Haycraft's curves indicates that in all
cases the end portions of the spectrum are at illuminations
calling for lower critical speeds than the low curve obtained
by the writer. Curve C, fig. 1, corresponds to 18 cycles
per second, while Haycraft's speeds vary from 19 to about
4 cycles per second. After noting this fact an additional
critical frequency curve (Curve D) was determined for an
illumination less than a tenth that of Curve 0. This shows,
with respect to the one at 5 I. XL, a pronounced Purkinje
shift, in qualitative agreement with Haycraft.

Apparently, therefore, the changes which accompany
decreasing illumination are first in one direction and then
in the other. In searching for some other phenomena of
critical frequency with which this might be coordinated, it
occurred to the writer that the regions of the Purkinje and
the reversed Purkinje effect might be connected with the

356

Mr. H. E. Ives on the

two different logarithmic rates at which critical frequency
varies with illumination. Porter * has found for white
light that the relationship n = k log. I +p represents the
critical frequency phenomena, where n= critical frequency
in cycles per second, 1= illumination, k and jt? are constants.
The constant Jc has, however, two different values, one below
e25 M.C., another above that illumination. When plotted
on semilogarithmic paper this relation is shown by two
' straight lines of different inclination meeting at *25 M.C.
It has been surmised that this illumination represents the
point of change from cone to rod vision.

Fig. 3 gives the results of a determination of these

Fig. 3.

o to ?0

Critical Frequency-Tlluminatiou Relations for " White " Light.

straight lines with the author's apparatus for the " white "
light of the standard carbon lamp. The abscissae are
logarithms of illumination units (metre candles on magnesium
oxide surface, viewed through artificial pupil of 1 sq. mm.)f ;

* Proc. Roy. Soc. Ixxix. p. 313 (1902).

f The illumination is that given by the intensity of the light source
divided by the square of the distance. The illumination upon the
retina, when the disk is in motion, corresponds to a steady illumination
of half the plotted values.

Photometry of Lights of Different Colours. 357

the ordinates are critical frequencies in cycles per second.
The three circles B, C, and D show the illuminations at
which the three critical frequency luminosity curves were
obtained. The reversed Purkinje effect occurs in the upper
or '* cone " region, the Purkinje effect in the lower or
" rod " region. In Haycraft's work the ends o£ the spectrum
were always in the " rod 93 region, so that the reversed
Purkinje effect would show itself only as a warping of the
medium illumination parts of the curves by an amount
easily to be mistaken for errors of measurement.

Before leaving consideration of fig. 3 attention is called
to curve N. This was made without the artificial pupil of
1 sq. mm. aperture. It furnishes a means of evaluating the
" illumination units " here used, in terms of metre candles
illumination of the standard white magnesium oxide surface.
To reduce illumination units to metre candles it is necessary
to divide by from 7 to 8 over the range of these experiments.
This figure of course applies to the writer's eye, and will be
different for other eyes in proportion to the relative natural
pupillary apertures of different observers. Since in working
with critical frequencies the field is illuminated for only one
half the time, the flicker and equality of brightness illumi-
nation units should be doubled in order to use this diagram.

While the discovery of the relation of the Purkinje effect
and its opposite to the two regions previously found by
Porter is a distinct step, further insight into the phenomena
follows from more detailed study. On examination of this
data it is obvious that the facts presented point to different
critical frequency-illumination relations for different colours.
Moreover, the relation in the rod region must be different
from that in the cone region, the change taking place at
about 2*5 I. U.

To test this hypothesis a set of critical frequency
determinations was made for various spectral colours.
Illuminations were reduced by neutral tint screens * placed
over the spectroscope slit. The results shown in fig. 4 bear
out the surmise. In the " cone 33 region the different
colours give straight lines (to within the errors of measure-
ment) which are differently inclined in such manner as to
give the reversed Purkinje effect. At critical frequencies
of from 18-12 cycles per second these lines change their
directions. Their new relative inclinations are such as
to give the true Purkinje effect. The most remarkable

* " A Form of Neutral Tint Screen," Herbert E. Ives & M. Luckiesh,
Phys. Review, May 1911.

Phil Mag. S. 6. Vol. 24. No. 141. Sept. 1912. 2 B

358

Mr. H. E. Ives on the

curves are those for deep red ('650 yu,) and for blue (*480 p).
The red curve maintains its direction. The blue curve
changes from a diagonal to a horizontal line ; that is, the
critical frequency becomes a constant, independent of illumi-
nation. The behaviour of the other colours is intermediate.

Fig. 4.

Critical Frequency^Illumination Relations for Different Colours.

A simple relationship therefore exists between the
luminosity curves at different illuminations, as given by
this method. In the region above the change of direction
we have, if Sx is the slit-width at X, F the critical frequency,
F = K\log Sx + Px, where Kx is a constant involving the
relation between critical frequency and intensity of radiation
for the individual eye for the colour in question and for the
size of the photometric field, and where Px is a constant
involving the quantity of energy emitted by the source
and the dispersion and dimensions of the instrument of
observation, as well as the relative sensibility of the observer's
eye to flicker at different colours at a given speed. In short,
the law found by Porter holds for different colours if the
values of the constants are changed in the equation expressing
the law. Upon determining the inverse luminosity curve
or slit-width curve for any chosen critical frequency,
knowledge of the constants Kx enables one at once to
construct the corresponding curves for any other critical
frequency. This may be done graphically, by determining

Photometry of Lights of Different Colours. 359

the straight lines of fig. 4 and plotting them in such units
that afc certain critical frequencies the values of Log. I are
the logarithms of the experimentally determined slit-widths.
The slit-widths for any other critical frequency (and hence
illumination, by reference to the line given by the standard
light source) may be read off the plot by laying a straight
edge parallel to the axis of abscissae at the desired critical
frequency.

From the standpoint of the present investigation the chief
interest in the study of the method of critical frequencies
lies in the light it throws on the flicker photometer. For
the sensibility of the method is too low for it to claim a
place in accurate photometry, a matter which is discussed
later. Does any simple relation similar to that just founds
exist between the flicker photometer luminosity curves at
different illuminations ? A number of similarities between
the critical frequency and the flicker photometer curves point
to their close relationship. They both show the reversed
Purkinje effect. The luminosity curves are at least approxi-
mately alike. Moreover, a peculiarity of the low illumination
flicker curves given in the last paper, which apparently was
an anomaly, is in accordance with the critical frequency
phenomena. The point referred to is this : in the curve
for the lowest illumination at which it was fouiad practicable
to work with the flicker photometer, the red side starts to
decrease in brightness — that is, to give a Purkinje shift —
while the blue side is still decreasing, thus resulting in a
narrowing of the curve. Examination of the critical
frequency plots of figs. 3 and 4 shows that the bend in the
" white " curve occurs at a higher illumination (or critical
frequency) than for blue, and at a lower illumination than for
orange and red. Consequently, if the white light curve be
taken as a reference standard, the change of relative direction,
constituting the shift from the reversed to the true Purkinje
effect, occurs sooner for red than for green or blue, precisely
what was observed.

Can the flicker photometer be considered merely as a
device for equating two flicker sensations which are dove-
tailed one into the other ? The similarities just considered
would suggest this possibility. We may consider two ways
by which this equating could take place. Either the illumi-
nation determines the relative quantities of light which
measure equal ; or else the speed at which the flicker
photometer is run in order to make the colour alternation
just disappear determines these quantities. Both factors
may play a part, and others may enter as well.

2 B 2

360

Mr. H. E. Ives on the

Let us consider the measurement of spectral colours
against one taken as the standard of illumination, or against
a white. On the critical frequency-log. I diagram, the
standard and the colours to be measured are each represented
by straight lines. At a given illumination a quantity of
any coloured radiation may be chosen such that flicker will
disappear with it at the same speed as with a chosen standard.
If the rise and fall or the contour of the flicker sensation is
independent of the speed or changes in the same manner
for all colours with change of speed, then this coloured light
may be alternated with the standard, and the speed may be
reduced to the point where colour flicker is just about to
appear — forming a flicker photometer. The speed not
altering the equality of the two contours, the relative
quantities of the standard light and the coloured will be the
same as was required to make flicker disappear with each
separately at the critical frequency for the standard. If
this is the state of affairs the same relationship between
critical frequency and slit widths exists for both standard
and colour in the flicker method as with the method of
critical frequency. That is

F = KslogI+ps,

F = K\ log Sx+^\.

We may then substitute for the critical frequency in question
its value in terms of the standard illumination, and obtain
as a result

KslogI + C = Kx logSx,

that is, the logarithms of the slit-widths will plot as a
straight line against the logarithms of the illuminations.

On the second assumption the relative quantities of the
standard and the coloured radiation would be read off the
diagram (fig. 4) for the speed at which the flicker photo-
meter is run. The possibility is, however, practically ruled
out by the fact that, as shown by reference to the data of
the first paper, the flicker photometer speeds for an illumi-
nation showing a strong reversed Purkinje effect are 8 to
10 cycles per second ; therefore, from the data in the
present paper they are well down in the Purkinje region.
Speed cannot therefore be the dominant factor.

Considerable time and care have been spent in testing the
first possibility. The data in the previous paper were plotted
lo S\

in the form of ]Qg g ^ against log I. The resultant lines

Photometry of Lights of Different Colours. 361

were so nearly straight as to raise expectations that the law
of the flicker photometer had been found. To obtain a more
conclusive test, isochromatics were then made. The spectral
colour and the standard were matched by the flicker photo-
meter at a series of illuminations, stepping down by means
of carefully calibrated neutral tint screens. On plotting the
logarithms of the slit-widths * against the logarithms of the
illumination, the curves of fig. 5 were obtained. These are

Fig. 5.

Sl/t w/dff>s w terms of 'ra/e/e a/. S60I.U. P/offed loqar//fim/ca/ty

Isochromatics, showing variation in relative brightness of spectral
colours due to variation of illumination, Flicker Photometer.

not straight lines. The simple law anticipated does not
hold. However, the effect of change of illumination is
shown in a manner which indicates the method of study by
isochromatics to be an excellent one for following the course

* For greater certainty slit-widths were not used in this case. Instead
the voltage of the test lamp was altered, the intensity change being first
determined for each colour by a spectro-photometer in which a variable
sector disk took the place of the usual variable slit.

362

Mr. H. E. I ves on the

of the Purkinje and similar phenomena. It shows the
rationale of changes which might, if obtained by another
method, be considered within experimental errors.

The curves show the reversed Purkinje effect, making
clear that the phenomena of the method of critical frequency
dominate in the flicker photometer. But instead of the
expected straight lines the nearest approach to them lies in
the long, rather flat curves of the middle of the spectrum,
while at the red and blue ends a double curvature indicates
a marked deviation at high illumination from the form to be
expected.

Two possible explanations of these deviations claim
attention. First, that the critical frequency phenomena
when plotted logarithmically are not really straight lines,
but curves, and that the flicker method actually agrees with
the other, but by reason of the greater accuracy of the
method shows the curvature clearly. Second, that while
the critical frequency phenomena are true straight lines as
plotted logarithmically, the flicker phenomena are merely
similar and not identical.

The first explanation is not improbable, at least for the
medium and low illuminations. The deviations from straight-
ness are probably within the errors of measurement by the
critical frequency method. (The log scale of fig. 5 is many
times larger than that of figs. 3 and 4.) The lowest in-
flexion point of the red curves corresponds fairly well to
the illumination at which this should occur according to
fig. 3. At higher illuminations the flicker photometer
results would be explained if the separate critical frequency
curves showed a tendency to bend to the horizontal, the blue
showing the greatest tendency, the red the least, with white
lying between. Fig. 6 shows red and blue curves, each the
mean of several sets in which the eye was rested in total
darkness for several minutes between each set of readings.
Under these conditions the higher illuminations produce
strong complementary after-images. These curves do exhibit
the bending suggested and also much more for blue than for
red. It may probably be explained as a fatigue or contrast
effect. However, an extended series of such measurements
showed that the occurrence of the change in direction is
somewhat dependent on the condition of the eye, and is not
nearly so easy to observe with white as with coloured light.
It is also probably dependent on the character of the photo-
metric field. The small bright area of the prism face
surrounded by an entirely black field may be expected to
cause contrast and induction phenomena which would oe

Photometry of Lights of Different Colours. 363

absent under less extreme conditions. It may be much
more marked under the doubled illumination which holds
when two colours are matched in the flicker photometer.

Fig. 6.

Critical Frequency-Illumination Relations for large and small
Photometric Fields.

I£ the latter supposition is correct it virtually means the
adoption of the second explanation, namely that the critical
frequency phenomena probably follow the straight line
relationship, and that the flicker photometer, influenced by
various factors, merely follows this relationship closely but
not exactly. In fig. 1, curve A, taken at a higher illumination
than those previously mentioned, the critical frequency
curve shows a larger shift toward blue than does the
flicker, while in curve C the shift toward red is greater.
Both these differences are near the limit of accuracy of the
measurements, but are consistent in indicating that the
flicker photometer method does not follow the critical
frequency method absolutely. On the whole it appears
more probable that the critical frequency phenomena do
obey the simple law given above and that the flicker photo-
meter phenomena merely approximate thereto. Other
factors, such as speed, mutual action of different colours,

364

Mr. H. E. Ives on the

perhaps the influence of the surrounding field, enter in the
latter case to cause deviations from the simple conditions.
At any rate the simple law which it was hoped to find does
not hold for the flicker photometer.

The actual effect of this deviation from the simple law is
to cause apparent constancy of the flicker curve at moderately
high illuminations, since the changes over a long range of
intensities are of nearly the order of the error of reading.
It must not be forgotten too that these data are all for a
large photometric field. Data for a small field are given in
fig. 5 by the dotted lines. Their much greater constancy of
value is noticeable.

A similar test of the method of equality of brightness
was made by plotting both the writer's data and Koenig's
in terms of log I against log. slit-width, and some iso-
chromatics were tried. Here again long curves were obtained.
If any simple law holds with regard to these phenomena it
is not this logarithmic relation, which, it may be noted, is of
course merely Fechner's law.

Small Photometric Fields.

Fig. 6 shows red and blue critical frequency data for a
small photometric field (diameter 10,9). The effect of
reducing the field size is to swing the blue line around
nearer parallel with the red. which is swung but little.
The reversed Purkinje effect will therefore be less, a condition
similar to that produced in the flicker photometer by the
same change of field size.

The most interesting point shown in the figure, however,
is the behaviour of the blue at very low illuminations. The
violent change of direction which occurs with a large field
either is absent or is pushed down to a lower illumination
than here tried. The fovea behaves toward blue light just
as the larger area of the retina behaves toward red. This is
in line with the finding of Koenig that the fovea is blue-
blind. It is here found to be not strictly blue-blind but
blind to the gray sensation which replaces blue at low
illuminations for a larger or peripheral field. There is also
some indication that the red small field curve tends to turn
at low illuminations in somewhat the manner of the blue
curve for large fields. The bearing of these points on colour
vision is discussed shortly.

An outstanding difference between Haycraft's work and
the present research may be noted here. While his results
are qualitatively explained by the data of fig. 4, these data
would not give his curves. Blue light attains a fixed critical

Photometry of Lights of Different Colours. 365

frequency of about 12 cycles per second, while Hay craft
worked as low as 4 or 5 cycles per second. The explanation
may be sought in two facts : his work was done with the
eye in an extreme condition of dark adaptation brought on
by one hour's rest in the dark before observations, and a
very small photometric field was used. That the constant
frequency attained by blue light depends upon the condition
of the eye is shown by the different values in figs. 4 and 5,
while the work on small fields shows that the turning point
may be depressed by restricting the area of the retina. The
combination of these two factors is probably sufficient to
explain the different values of critical speeds at which the
same phenomena occur in the two investigations. Pecu-
liarities of the individual eyes, such as differences in the
relative proportions of rods and cones, might also be of
influence.

Sensibility of the Critical Frequency Method.

Photometry by the method of critical frequency is con-
siderably less accurate than by either the equality of
brightness or the flicker method. From among the sets
of readings made near Ihe close of the investigation one
day's observations on " white 33 light were selected at random
and studied with the following result : At a high illumination,
corresponding to 43 cycles per second, the average deviation
from the mean of twenty settings was 1*8 per cent, in speed ;
at 32 cycles per second, 1*9 per cent, in speed ; at 23 cycles,
1*9 per cent, in speed. These errors appear small, but when
expressed in terms of brightness instead of speed they are
found to be too large for accurate photometry. They
correspond respectively to 18 per cent., 14 per centv and
10 per cent, in brightness, or five or ten times the mean
error by the flicker method. Settings made on different
days, or on the same day with the fatigued and unfatigued
eye, are apt to differ by two to three per cent, in speed.

The critical frequency method is highly subject to dis-
turbances whose explanation is physiological or psychological.
Depending on whether the eye has been rested in diffused
light, in darkness, or by blindfolding, the absolute values of
the readings will be increased or decreased throughout the
spectrum *. Some experiments made during the period
covered by this investigation indicate that these changes
may affect an unsaturated colour more than a saturated one,
or less. This would cause the area of the luminosity curve
to be in error.

* F. Allen, Phys. Rev. 1900 & 1909, loc. cit.

366

Mr. H. E. Ives on the

The slopes of the straight lines, obtained by plotting, as in
fig. 3, are subject to variations, in general of such a nature
as would be caused by variations in the size of the field,
indicating a changing balance between rods and cones. A
rather curious difference in the setting depends on whether
the variable be speed or brightness. If the slit-width for
any colour is held constant the critical speed may be found by
several settings. If this speed is held and the brightness
varied by changing the slit till flicker vanishes, the value
obtained from settings for slit-width may differ as much as
15 or 20 per cent, from the previously fixed value, an effect
apparently acting one way at one period and another way at
another. This disturbance affects all the spectral colours to
the same extent (as nearly as can be judged) so that a curve
of larger or smaller area results depending on the method
of setting.

In view of this fact the critical frequency curves of fig. 1,
curves A to D were made by speed settings alone (except D).
First the critical speed for the standard lamp illumination
was determined ; then, with the slit set at the value given by
the previous flicker photometer setting, the critical speed
for the colour was determined. From the log I-critical
speed relations previously determined the equivalent change
in slit- width was read off. The relative values for the
different colours, that is the shape of the curves and the
Purkinje shift, were as previously obtained by the procedure
described above, but these curves are given as being freer
from objection.

Great care is taken in the present paper to draw only
such conclusions as are warranted by the accuracy of the
method.

The Areas of the Curves.

Because of the small sensibility of the critical frequency
method and its susceptibility to obscure disturbing factors,
it is hard to draw very definite conclusions from the difference
of area shown between certain of the critical frequency
curves and the flicker and equality of brightness curves.
Suffice to say that such differences are apt to occur and that
the previously found differences of area between the flicker
and equality of brightness curves again appear *. These
are sufficient to show the futility of concluding that different
photometric methods give identical results simply because

* In fig;. 1, curves A, the equality of brightness area is smaller than
the flicker, a condition not previously found at this illumination

Photometry of Lights of Different Colours. 367

they show the same distribution of brightness in the spectrum.
The capacity of different methods to summate will form the
subject of a subsequent paper.

Peripheral versus Central Vision.

The greater sensibility of the peripheral retina to motion
and to flicker has been frequently observed. In the work
on the flicker photometer the possibility of using this greater
peripheral sensitiveness was investigated, with the unexpected
result of finding a smaller sensitiveness than for central or
foveal vision. During the course of the present work
frequent comparisons were made between central and peri-
pheral sensitiveness to flicker, with different colours, and
with large and small fields, at different illuminations. The
findings explain satisfactorily the failure of peripheral vision
with the flicker photometer.

The most significant fact was learned on the failure of
several attempts to secure the critical frequency-illumination
relationship by peripheral vision settings, namely, that such
greater sensitiveness as the periphery possesses quickly
disappears on continued gazing. It is, at least at medium
and at high illuminations, merely a momentary phenomenon,
not at all available for careful and continued photometric
settings. The periphery, by the fatigue due to steady use,
becomes for the long wave end of the spectrum, and at high
illuminations, less sensitive than the centre of the retina.
The fovea alone appears to have properties sufficiently
constant and dependable for photometric use.

After this fact was established qualitative observations
were carried out, with the eye thoroughly rested between
observations. The critical speed for central vision was
established, the eye was directed so that the image fell about
7° from the fovea, usually on the nasal side, and the direction
of change of speed necessary to produce or destroy flicker
was noted. These observations showed that for very high,
nearly dazzling illumination, there is little choice between
centre and periphery with red and blue light, with large or
small field. A large retinal field is always more sensitive
than a small one, apparently a pure area effect.

At lower illuminations the periphery becomes more and
more sensitive to blue flicker, but less to red flicker. At
very low illuminations (about 12 cycles per second) with a
small field the difference between the behaviour of the two
colours is enormous. By direct vision a blue field is almost
invisible and flicker is perceived only at a low speed ; by

368

Mr. H. E. Ives on the

peripheral vision the field flashes out brilliantly, and simul-
taneously a flicker of large amplitude appears. For red
light these conditions are reversed ; it is now the periphery
which is less sensitive to light and flicker. This behaviour
of red and blue light at low illuminations has been previously
noted by Dow *.

Bearing upon Theories of Colour Vision.

Koenig in his study of the visual purple found its absorp-
tion spectrum to correspond to the luminosity of the spectrum
at very low illumination, i.e., twilight or colourless vision f.
The product of its decomposition, the visual yellow (which is
in turn decomposed) has an absorption spectrum corre-
sponding to the distribution of the blue sensation at high
illuminations. Study of the red, green, and blue sensation
curves with continually decreasing illumination X shows that
the colourless sensation at low illuminations arises by gradual
transformation of the blue sensation — the red and green
retaining their distribution substantially unaltered. At high
illuminations, therefore, gray or white is a mixture of three
colour sensations (using the word sensation in Kcenig's
meaning), while at low illuminations the gray sensation is a
simple one due to the transformed blue remaining after the
red and green has dropped below the threshold. At high
illuminations Koenig considers the visual purple to be broken
down successively into visual yellow and the final colourless
product ; at low illuminations only the first transformation
takes place. Visual purple occurs only in the retinal rods,
and is absent from the cones, consequently from the fovea.
The fovea he finds is blue-blind.

In the first paper of this series it was suggested that the
retinal cones or colour-seeing organs might be responsible
for the behaviour of the flicker photometer. It was assumed
that the peripheral cones, which are large, might be more
red-sensitive ; that is, more extreme in their cone character
than the foveal cones. Situated among the rods, their
exaggerated red-sensitiveness might with decreasing illumina-
tion tend to partly counterbalance the increasing part played
by the rods. In the flicker photometer these cones acting
alone (due in some way to the intermittent stimulus) produce
the reversed Purkinje effect. Could the rods be made to act
alone, an abnormally large Purkinje effect would result.

* Phil. Mag. Jan. 1910, p. 58.

t "Ueber den Mensclilichen Sehpurpur," Gesammelte Abhandlungen,
p. 338.

\ E. Tonn, Zeit.f. Psijch. u. Phys. vi. p. 279 (1894).

Photometry of Lights of Different Colours. 369

In the equality of brightness photometer (corresponding to
ordinary vision) the rods and cones act together, the former
prevailing at low illuminations.

The new facts learned in the present investigation seem to
be in accord with the work of Koenig and this suggested
mode of action of the flicker photometer. We must add to
the hypothesis, just reviewed, the assumption that the blue
sensation, although produced in the visual purple of the rods,
behaves in a similar manner to the red and green sensation
localized in the cones. It is not necessary to assume an
exaggerated sensitiveness in the peripheral rods because the
greater number of rods will alone account for that. We
have then at high illuminations colour vision, and response
to intermittent stimuli as represented by the logarithmic
relation discussed above. This state is due to cone action
and visual yellow decomposition. At a certain low illumi-
nation we cease abruptly to have blue vision. In its stead
we have colourless vision obeying an entirely different Jaw
with respect to flicker and ascribable to the incomplete
breakdown of visual purple. In accordance with this
hypothesis is the fact that the violent change of direction in
the blue line of the log I-critical frequency diagram, is
coincident with the change in appearance from blue to gray.
Also the observation, in confirmation of the statement of
Koenig and others, that red light does not change to gray
but continues red until the lowest illumination possible
to make observations. The different behaviour of blue light
for a small or a large field at low illumination is also in accord
with the anatomical fact that the rods are missing in the
fovea, and with Koenig' s observation of foveal blue blindness.

Summary,

1. Spectral luminosity curves obtained by the method of
critical frequency show a reversed Purkinje effect, but at
very low illuminations a true Purkinje effect, the latter
observed by Haycraft.

2. A plot of critical frequencies against the logarithm of
the illumination for white light gives, as found by Porter,
two straight lines of different slope, which meet at about
2*5 I.U. The reversed Purkinje effect occurs above this
point, the true Purkinje effect below it.

3. When separate colours are investigated and plotted in
the above manner, a set of straight lines of differing slope
results.

4. At about 2"5| I.U. these lines in general change their

370 The Photometry of Lights of Different Colours.

slope, but while the line for deep red does not change, that
for blue becomes horizontal, or critical frequency becomes
independent of illumination. The Purkinje effect and its
opposite follow at once from these facts.

5. The flicker photometer is shown to be largely influenced
by the critical frequency phenomena, but not to obey the
simple law which would follow were it a mere dove-tailing
of two pure flickers.

6. The peripheral retina is found to be more sensitive to
flicker only for momentary observation before adaptation or
fatigue sets in. The fovea is more sensitive to red flicker,
the periphery to blue, and the difference is more striking at
low illuminations, as noticed by Dow.

7. The phenomena of critical frequency are in general
accord with Koenig's theory of the function of the visual
purple and with the hypothesis that the retinal cones are
chiefly active in the case of intermittent or alternating
stimuli.

Physical Laboratory,
National Electric Lamp Association,
Cleveland, Ohio.

January, 1912.

From the Philosophical Magazine for November 1912,

Studies in the Photometry of Lights of Different Colours. —
III. Distortions in Spectral Luminosity Curves produced
by Variations in the Character of the Comparison Standard
and of the Surroundings of the Photometric Field. By
Herbert E. Ives.

A PREVIOUS paper in this series described spectral
luminosity curves obtained by the equality of bright-
ness and flicker photometers. The mean of the high
illumination values as obtained by rive observers showed
close agreement between the two photometric methods,
although the relative positions of the equality of brightness
and flicker curves varied among the different individuals.
In the same paper attention was drawn to the fact that these
measurements covered only a special case, namely, that of
comparison of the spectral colours against a single compari-r
son source — the unsaturated yellow of the carbon incandescent
lamp. Certain experiments there quoted raised the suspicion
that the luminosity curve obtained might be to some extent
a function of the colour and saturation of the • comparison
standard due to the accentuation of colour by simultaneous

745

Mr. H. E. Ives on the

contrast. As this limitation of conditions also held in the
work of Koenig, who used wave-length "535 fi as his com-
parison light, and of Abney who used " white," it is a matter
of some interest to learn whether this suspicion is upheld or
not. The experiments here described give the answer to the
question at issue. Tn addition, another question is investi-
gated, namely, whether an alteration in the surroundings of
the photometric field, from dark to light, disturbs one's
judgment of equal brightness.

In the first of these experiments no change was made in
the apparatus as previously described except that red and
green glasses were used in connexion with a high intensity
(400 cp.) source in order to obtain red, green and " white "
comparison illuminations of the same brightness. The red
light corresponded in hue to '62 yu,, the green to *55 fi. With
these three colours luminosity curves of the spectrum were
made under substantially the conditions of the earlier experi-
ments. Two illuminations were used, a high one of 300
illumination units, a low one of 10 units ; two field sizes
were used, one of 1°#85 diameter, the other 5° x 8° ; the
readings were in terms of slit-widths to give equal brightness.
The source measured was a normally operated tungsten lamp,
as before, but since the results recorded are entirely com-
parative no values are given for its energy distribution, nor
are corrections made for prismatic dispersion.

The results obtained were strikingly different in character
by the two photometric methods. By the equality of bright-
ness method a series of different luminosity curves were
found, a different one for each colour of comparison standard.
These curves vary from each other by amounts as great as
would be caused by considerable differences in illumination
for a single comparison standard. One of the most significant
things about these curves is that no system or regularity has
been found in their manner of deviating from " normal.5' For
instance, in fig. 1 (p. 746), where are plotted a set of selected
characteristic curves from this series (for high illumination),
it will be seen that two made with a green comparison light
at different times lie at the two extremes of character.
There is not a shift in one direction for a green standard,
and in the opposite for a red, but apparently any sort of shift
may be expected in changing from one comparison light to
another.

It is a common experience in heterochromatic photometry
to form a fairly constant criterion of equal brightness when
working with a definite set of colours. It is easy to imagine
that such a criterion when formed must have some claim to

Photometry of Lights of Different Colours. 746

be considered " correct." The previous work of the writer
cast doubt on this belief, since the equality of brightness
luminosity curves were found to change their shape and
position after intervals of time sufficient to destroy one's

Fisr. 1.

•SO '5Z -54- -56 -5Q -60 -62 -64- '(.bft

memory of previous settings. The present work seems to be
conclusively against the belief that a " correct 99 criterion of
equal brightness may be attained by mere practice. While
with any given comparison source quite definite and con-
sistent spectral luminosity curves may be obtained, these
experiments show that after working with several different
comparison sources, a return to the first one does not mean a
return to the original criterion. It appears therefore that
the differences introduced by changing the standard of com-
parison must be looked upon as psychological. One's judg-
ment is disturbed, and the part played by judgment in the
case where different colours are matched for brightness may
be very large. The results plotted in fig. 1 are for high
illuminations and small field ; similar results were obtained
for the other conditions of illumination and field size.

These remarks apply only to the equality of brightness
method. The curves obtained by the flicker method showed
no deviation from each other which could with certainty be
considered greater than the errors of measurement. In fig. 1
therefore is plotted a single flicker curve. The equality of

747

Mr. H. E. Ives on the

brightness curves are grouped about it in a manner to suggest
that it is the true normal of which they are all distortions.

The second set of experiments performed was to study the
effect of changing the surroundings of the photometric field.
It was suggested to the writer by a psychologist that the
ordinary optical instrument using a telescope subjects the eye
to an abnormal condition in that the field of the instrument
is surrounded by a totally black space. Under normal con-
ditions, on the other hand, the whole retina is active. Such
an abnormal condition might be expected to disturb such an
unstable thing as an equality of brightness judgment.

In order to study this problem the telescope tube of the
spectrometer was removed. The eye-slit was attached to a
separate rigid stand, the object-glass was held in its original
position by a different means. Against the objective were
laid large flat metal plates pierced by openings of a size to
give the same effective photometric fields as in the previous
experiments. These plates were smoked with magnesium
oxide and arrangements were made to illuminate them, when
in place, by two incandescent lamps whose intensity could be
controlled by a series resistance. The plates were of such
size that upon turning on the incandescent lamps the whole
field of view, except as limited by the ocular slit, was bright.
This meant a field of approximately fifty degrees and was
considered ample to test the matter in question.

A series of luminosity curves under the same conditions as
previously obtained w ere made, except that both light and
dark surroundings were tried. Again the results were in
marked contrast as obtained by the equality of brightness
and flicker methods. By the former method different curves
result depending on the character of the surrounding field.
But here, as before, no systematic relationship exists in the
curves under the two conditions. The effect of changing
the surrounding field from dark to light is to introduce a
shift or distortion which may apparently be in either direc-
tion. It is again a case of disturbed judgment. In fig. 1
the effect of a light surrounding field as found in one instance
is given. With the flicker method, on the other hand,
changing the surrounding field introduces no variations
certainly larger than the errors of setting.

Before leaving the experiments on light and dark sur-
roundings some incidental results may be noted. With the
small field, using the equality of brightness method, a very
considerable increase in definiteness of setting was found
with the bright surrounding field. A similnr increase was
not found with the large field, nor by the flicker method, but

Photometry of Lights of Different Colours. 748

in the latter a bright surrounding field necessitated a higher
speed for the rotating disk. Although no certain increase in
sensibility appeared, considerably greater comfort was felt
in working with the larger area of retina active, which would
recommend that condition for accurate work if a small field
is used.

At low illuminations with a large field where the Purkinje
effect appears in the equality of brightness method, and the
opposite effect by the flicker method, an interesting question
is whether these effects are to be connected with the exci-
tation of a large retinal area or only with the area which is
concerned with the actual comparisons of brightness, or
detection of flicker. In short, at low illuminations, will
surrounding a small photometric field with a large brigtit
area be equivalent to using a large photometric field ? The
answer is in the negative, for while bright surroundings
shift the equality of brightness curves, the shifts are neither
in direction or amount consistently such as would be called
Purkinje shifts, and with the flicker method the absence of
any shift disposes of the question at once.

It is evident from these experiments that no reliance may
be placed upon an equality of brightness luminosity curve
obtained under such conditions that the psychological
element of the judgment of equality of essential inequalities
is necessary. The fact that the flicker photometer is free
from such uncertainty is a strong argument in its favour.
There still remains unsettled, however, the question whether
the flicker photometer gives something that may with pro-
priety be called the true brightness. In other words, does
it give what would be obtained by the equality of brightness
method with the psychological variables eliminated ?

This query naturally leads to the consideration of a method
of heterochroniatic photometry which has been advocated
and used in certain cases, namely that by steps of small hue
difference, or in cascade, as it is sometimes called. The
principle is that if the hue difference is made small enough
it will not disturb the brightness judgment. In establishing
incandescent lamp photometric standards of different colour,
this method is particularly feasible, since all intermediate
colours are obtainable by voltage variation.

In order to obtain spectral luminosity curves by this
method, two additions were made to the apparatus as
previously described. First a second spectrometer similar
to the first, but with its telescope removed, was added.
A first surface platinum mirror, obtained by cathode depo-
sition on a piece of glass, which was afterward cut in two

749

Mr. H. E. Ives on the

to make a sharp edge, was placed directly behind and
parallel to the rotating disk, and so arranged that it conld
be drawn np out of place. The second spectrometer was
then so placed that the light from its prism was received
by the mirror and reflected into the telescope of the original
instrument. In this way half the field received light from
each instrument, and any two spectral colours could be
compared by the equality of brightness method. The flicker
disk and comparison lamp being undisturbed, it was possible
at any time to secure a flicker photometer curve. As these
were proved to be independent of the kind of comparison
lamp used, it was not necessary to arrange to secure such
curves for different spectral comparison colours, as might at
first sight have been thought necessary for completeness.

These experiments were carried out only at the high
illumination for the small field size, and with a bright
surrounding field, these being the conditions dictated by all
the work up to the present as best for accuracv and freedom
from disturbances of all sorts, and so best fitted to be estab-
lished as standard. Starting at the middle of the spectrum,
the two sides of the field were made alike in hue and closely
the same in brightness, and their relative brightness measured,
then one side was changed to a wave-length only slightly
removed and its brightness was measured, the wave-length
difference being such as to introduce only a very slight hue
difference. The comparison field was again made like the
test side, the latter moved to a new wave-length and the
brightness of this step compared with the first, and so on
through the spectrum. Then starting at either end with the
slit-width values obtained by working from the centre, the
spectrum was measured continuously to the other end.

The curves obtained by this procedure were unsatisfactory,
because of cumulative errors. Upon returning from red to
blue, after working from blue to red, the original value for the
end of the spectrum was not obtained. In order to eliminate
all possibility of systematic drift such as might be caused by
favouring the new hue, or one side of the photometer field, the
followino- scheme was substituted for the first : — At numerous
points in the spectrum, at the approximate slit-widths found
from the mean of the previous work as necessary for equal
brightness, the ratio of brightness of X to X— AX was
measured. For AX was chosen '004 /ll, which means every-
where a very small hue difference. The measurements
were made at points taken absolutely haphazard, and each
measurement consisted of four, first with both sides of the
field illuminated by X : second, the right-hand side by X,

Photometry of Lights of Different Colours. 750

the left by X — AX; third, both sides by X — AX ; fourth, the
right-hand side by X— AX, the left by X. From these two

values of the ratio - — — r^- were obtained and their mean

X — AX

was adopted. These values were plotted as a curve, and
from this was built up the luminosity curve shown in fig. 2,

Fig. 2.

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a curve which may fairly be claimed to be independent of
the psychological errors illustrated by fig. 1.

After obtaining this luminosity curve, a flicker curve and
an equality of brightness curve, by the ordinary method,
against incandescent lamp light, were made. These are
shown as well in fig. 2. It will be seen that the flicker
curve (circles) agrees with the special small step equality
of brightness one. The ordinary equality of brightness
curve happens to be quite different from the flicker curve.

This result is in agreement with the conclusion drawn
from the previous work with five observers, that when the
psychological errors are eliminated the equality of brightness
and the flicker photometers agree at high illuminations.
Tn the one case an attempt was made to eliminate the
psychological difficulty by taking the mean of several dif-
ferent observers, in the second case by a special method of
observation. In the writer's opinion these results justify
the opinion that the flicker photometer gives, under the
conditions specified, what may be considered the true
brightness.

751 Photometry of Lights of Different Colours.

It follows from this work that previously obtained spectral
luminosity curves, such as those of Koenig and Abney where
the equality of brightness method was used, are subject to
considerable uncertainties. While in the case of Koenig's
curves for different illuminations the amount and direction
of the changes constituting the Purkinje effect may be
substantially correct, the absolute values for the energy-
luminosity values cannot be considered as sufficiently exact
to be taken as normal. In view of the results of this paper
it is probable that the mean flicker curve given in the first
paper of the series is more entitled to be called a normal
luminosity curve than any previously obtained ones.

The main results of this paper may be summarized as
follows : —

1. With the equality of brightness method the effect of
changing the colour of the comparison field and of substi-
tuting light for dark surroundings to the photometric field
is to introduce irregular and unsystematic shifts and dis-
tortions of the spectral luminosity curves.

2. With the flicker method, the corresponding changes
produce no alterations in the luminosity curves.

3. The equality of brightness spectral luminosity curve
obtained by taking small steps of slight hue difference, agrees
at high illuminations, for a small field, with the curve given
by the flicker photometer.

4. It is concluded that the flicker photometer gives, under
the specified conditions, the true brightness.

Physical Laboratory,

National Electric Lamp Assoc.,
Cleveland, Ohio.

May, 1912.

From the Philosophical Magazine for December 1912.

Studies in the Photometry of Lights of Different Colours. —
IV. The Addition of Luminosities of Different Colour. By
Herbert E. Ives.

A WELL-NIGH indispensable requirement of a method
of measurement is that its renderings shall conform to
two geometrical axioms. The first of these is that things
equal to the same thing shall be equal to each other ; the
second, that the whole shall be equal to the sum of its parts.

In the majority of measurements performed in the physical
laboratory the quantities dealt with are of such nature that
conformity to these axioms is unquestioned. Among these
measurements fall those of illuminations of identical colour
and quality. But when the condition of complete identity
of quality in the compared quantities is departed from, as is
the case in the photometry of lights of different colour, it is
unsafe to assume that these axiomatic relations hold. This
paper discusses the methods of heterochromatic photometry
from the standpoint of these axioms. It is shown that only
one method — the flicker method — strictly conforms to the
requirements in question.

As to the first requirement, that things measuring equal
to the same thing shall measure equal to each other, the
subject matter of the previous papers of this series gives
complete information. By the methods of visual acuity and
critical frequency this is so, from the nature of the measuring-
process, in which no real comparison source — whose character
might be varied — exists. In the two remaining methods —
equality of brightness and flicker — the fulfilment of this
requirement reduces to this — that no change in the character
of the reference standard shall affect the relative brightness
of the different coloured lights under measurement. In the
case of spectral luminosity curves this means that the shape
of the curve must not be altered by a change in the reference
standard. In the last preceding paper of this series it was
shown that by the equality of brightness method various
distortions of the spectral luminosity curves may be expected
upon changing the hue of the reference standard. By the
flicker method such changes do not take place. Therefore
the first requirement mentioned above is met by the flicker
method, but not by the equality of brightness method. Two
different equality of brightness methods must, however, be
distinguished, the ordinary one, where large hue differences
are under comparison, and another, where by steps of small

846

Mr. H. E. Ives on the

hue difference the psychological element of appraisement is
eliminated. As was shown by the last paper, the latter
procedure gives results identical to the flicker method. In
the present paper, when equality o£ brightness is mentioned,
the straightforward method of comparison as usually carried
out with large hue differences will be meant.

As to the second requirement— the summational one — it is
to be borne in mind that while this presupposes the first one
fulfilled, it may fail even with that holding. The process of
physical summation may introduce factors which are not
present or magnify ones not significant in the separate parts.
An instance of this is given below. It is to be noted further
that certain differences may exist in the results of two
methods without any clash with this second requirement.
Speaking in terms of spectral luminosity curves, this means
that the curves by different methods may differ in the
position of their maxima, and may show different directions
of change with variation of illumination, but if they maintain
their areas the same may all conform to the requirement in
question. If, however, the areas of the luminosity curves
are different, then the sum of the parts cannot equal the
whole by all the methods under test. This is obvious when
one imagines the luminosity curve under measurement to be
that of a source identical with the comparison standard. If
at the end of the spectral measurement the dispersed light is
recombined, then, being identical in quality with the com-
parison standard, it must measure the same by all methods
of measurement. If by one method of measurement this
physical summation agrees with the arithmetical summation,
derived through the area measurement, it cannot agree with
others giving different areas.

As has been noted from time to time in these papers,
curves of different area are obtained by the different methods
of coloured light photometry. A striking example of this
is given in fig. 1, where are four luminosity curves obtained
at one sitting by the methods of visual acuity, critical
frequency, equality of brightness and flicker. While they
differ little in general shape and position of maxima, the
enormous differences in area illustrate forcibly the error
fallen into by assuming these methods identical on the basis
of the similarity in shape of curves obtained by different
observers. The most startling curve is the visual acuity one.
This was obtained by the use of a test object consisting of a
fine line grating placed over the telescope lens. Its area is
five times that of its nearest neighbour, which latter differs
only by a fractional part from the other two.

Photometry of Lights of Different Colours. 847

The enormous area of the visual acuity curve is at once
explainable as due to the chromatic aberration of the eye.

Fig. 1.

Simultaneously Obtained Spectral Luminosity Curves by four J
Photometric Methods.

o- — « v/suALACuirr \

K x EQUAL/ Tf OF BR/GHTNESS

~ FUCKER

■SZ >S4- -$6 -S8 *6o .6Z 6<h 66/i

It has been shown by Bell * and by Luckiesh f, in work
published since the first o£ these papers was written, that the
defining power of the eye is much greater for monochromatic
light than for complex light of the same hue. It may thus

* L. Bell, Elec. World, vol.lvii. p. 1163 (1911).

t M. Luckiesh, Elec. World, vol. lviii. p. 450 (1911).

848

Mr. H. E. Ives on the

easily happen — in the case of a purple composed of red and
blue light — that increase of illumination reduces the detail-
revealing power of the eye, although for the component
parts of the acting light the normal relation between visual
acuity and brightness holds. The visual acuity curve of
fig. 1 is therefore amilysable as a combination of the acuity-
brightness relation and what may be termed a quality factor.
It is a perfect example of a method of measurement in which
axiom 1 is valid, but not axiom 2. Needless to say, the
existence of such a quality factor effectually disposes of
the method of visual acuity as a method of measuring
brightness.

The differences between the remaining three methods are
probably due to more obscure psychological causes. In the
case of critical frequency the ease with which area differences
may be produced has been pointed out. The manner in
which the equality of brightness curves are disturbed by
varying the comparison standard is sufficient reason for
regarding without surprise the differences which have been
found between these areas and those by the flicker method.

The crucial test of axiom 2 appears to be, in the light of
all previous work, reduced to its test by the flicker method.
Such tests have been made by Whitman *, and later by
Tufts f. Since the latter's was more complete, the experi-
mental test which is described below was modelled upon his,
with, however, certain very essential modifications. A brief
account of his experiment is necessary.

Two identical incandescent lamps were chosen, one so
placed as to illuminate a white surface before the slit of a
spectrometer, the other so placed as to illuminate a rotating
sector in front of the telescope lens. The latter lamp was
placed on a photometer track so as to be movable. The
slit-width was held constant and the brightness of the
spectrum measured at several points by the flicker method.
At the end the prism was removed, and the brightness of the
total light through the spectrometer was measured against
the movable lamp. This was found to be within a few per
cent, the same as that indicated by the area of the luminosity
curve.

Further experiments showed the area of the luminosity
curve to be unaltered by observing through a coloured glass,
as it should not be if axiom 2 holds. When, however, a
deep cobalt blue glass was used a large discrepancy was
found. Certain other observers, who were less red-sensitive

* Whitman, Phys. Rev. iii. p. 241 (1896).
t Tufts, Phys. Rev. xxv. p. 433 (1907).

Photometry of Lights of Different Colours. 849

than Tufts, showed a discrepancy in the same direction even
with white light.

The points to which attention should be directed here are,
1st, that the conditions of illumination and field-size are not
stated, nor was the illumination constant. Instead of taking
portions of the spectrum of equal brightness, equal slit-widths
were taken, with consequent low illumination at the red and
blue ends. 2nd, there is no mention of correction for the
light lost by absorption and reflexion in the prism. It is
hard to imagine that this correction was not made, but the
test is inconclusive as long as this is in doubt.

With regard to the peculiar discrepancy with the deep
cobalt glass, this can be explained, qualitatively at least, by
the results of paper II. of this series. Bearing in mind that
the effect of this screen over the eye is to reduce the illumin-
ation excessively, it is quite possible that the spectral blue
measurements fell in the region indicated by the arrow in
the (slit-width) diagram sketched in fig. 2, in a region where

Fig. 2.

Suggested Explanation of Anomalous Results of Tufts.

Log. S!it--'y,dih

the law of the flicker photometer changes (see paper II. of
this series). The result of this would be the effect found by
Tufts. However, these low illumination effects, interesting
as they are in connexion with the theory of colour vision,
cannot be held of primary interest in practical photometry.

A repetition of this experiment is here described, in which
the undesirable features of Tufts' experiments are eliminated.
Because this work is intended primarily for application to
practical photometry no repetition is made of the low
illumination tests, nor tests on observers of abnormal colour
vision.

850

Mr. H. E. Ives on the

The apparatus used is that employed in the previous
investigations described in this series with certain modifica-
tions. An important feature is a special slit, made with both
jaws movable. One is moved by the divided head as before
(adjustable edge) ; the other is free and may be brought
into contact with the first by merely sliding in its ways.
The method of use is to leave the prism fixed throughout
the experiment ; the adjustable edge of the slit is placed in
a position corresponding to the ultra-violet, the free edge
brought into contact with it. The adjustable edge is then
moved by the divided head until, by the flicker criterion, a
piece of the spectrum is transmitted equal in brightness to
the comparison standard. The free edge is then brought up
into contact with the adjustable edge and another piece of
the spectrum of the same brightness exposed by moving the
latter. In addition to this slit another means of varying
the amount of spectral light is furnished by a variable
neutral tint screen * between the light source and the ground
glass over the slit. This is used at the end of the spectrum,
where the last portion of spectral light consists of the whole
remainder of the spectrum and cannot be varied in brightness
by slit-width variation. (This screen can of course be used
at any point if so desired in place of slit-width variation, it
being only necessary to take slit-widths of suitable size so
as to give approximately the same amount of light.) At the
end of the spectral measurements the free jaw is drawn back
to its original position, whereupon the eye-slit receives the
whole spectrum which it has before received in parts. The
prism used in this test was a special constant dispersion,
constant deviation type, made by A. Hilger. It gives a
considerably shorter spectrum than that furnished by the
regular crown glass prism used before.

A new form of flicker photometer was used in place of the
rotating disk of the previous work. This consists of a first
surface metal mirror on an oscillating lever. The mirror
was made by coating a glass plate with platinum by cathode
discharge, then cutting the glass with a diamond. The edge
where the glass breaks is almost invisible in the photometer
field f. The other end of the lever is driven by a link
motion attached to the speed counter axis and having a
1-inch stroke.

This mirror device gives a close approximation to a
perfect flicker photometer. With regard to the question of

* "A Variable Absorption Screen," Ives, Elec. World, March 16,
1912.

f Pfund, Johns Hopkins Univ. Circular, vol. iv. 1906, pp. 20-22.

Photometry of Lights of Different Colours. 851

perfection in flicker photometers, a word may be said. Some
experimenters have thought they found differences in the
results with the flicker photometer when it was operated at
different speeds. As a matter of fact there is only one speed
for such a photometer, namely, that which just causes colour
flicker to disappear. Any greater speed causes a decrease
of sensibility. Now as the colour difference is decreased a
decrease in speed and an increase in sensibility are made
possible. If there is no difference in colour, the speed drops
to zero. In other words, for lights of the same colour the
flicker photometer approaches as its limiting case the equality
photometer. In the instrument now described this is proved
to be literally so. By proper choice of voltages on the test
and comparison lamp, and by slightly tinging the light from
the latter by letting it fall upon a flashed opal glass over
which is laid four thicknesses of lantern-slide cover-glass,
the total spectral light, obtained from the wide slit, and the
comparison standard light, are identical in appearauce. The
speed for greatest sensibility is as it should be, zero.

Another detail of some importance is that in measuring
the total light through the prism a neutral tint screen * is
placed over the slit, of such transmission that it reduces this
light to approximately the same brightness as the comparison
standard, the exact setting being made by means of the
variable neutral tint screen before mentioned. The object
of this is to have all the measurements carried on at the
same brightness, although since this final measurement is
of lights of the same colour it is not perhaps absolutely
necessary.

It may fairly be claimed for this arrangement of apparatus
that physically the whole is exactly the sum of the parts.
There is no measurement of areas ; all scattered light is
present exactly in the same manner in the fractional and
total light measurements ; there are no instrumental changes
for which correction need be made, such as the removal of
the prism in Tufts' experiment.

Three sets of measurements were made. For each an
illumination of 300 I.U. held ; the field was 2° diameter,
and surrounded by a large bright area (25° diameter). Two
sets were made by the writer, whose luminosity curve lies
nearly at the blue extreme of the observers previously
examined, one set by Dr. P. W. Cobb whose luminosity
curve lies at the red extreme.

* " A Form of Neutral Tint Absorbing Screen," H. E. Ives &
M. Luckiesh, Phys. Rev. May 1911.

852

Mr. H. E. Ives on the

The results were as follows : —

By parts. Total.

H.E.I. 1 691 695

H.E.I. II 742 743

P.W.C. 1 773 785

(Slight changes in the position of the variable screen and
comparison lamp cause the different magnitude of the results
in the arbitrary units given.) The greatest difference is in
the case of the less practised observer and amounts to
1^- per cent. This lies within the range of his errors of
setting.

The conclusion is drawn that under the conditions of high
illumination and small field size specified, the arithmetical
sum of the parts as measured agrees with the measured value
of the whole, by the flicker method, for observers of normal
colour vision.

With the proof of this property of the flicker method of
photometry is concluded the set of tests which were planned
at the beginning of the investigation. A general summary
of the characteristics of the flicker method follows : —

1. It surpasses all other photometric methods in sensibility
and reproducibility in the presence of colour difference.

2. It agrees at high illuminations with the equality of
brightness method, when the latter is freed from the psycho-
logical uncertainties inherent in its use.

3. It measures at high illuminations what may fairly be
termed the true brightness.

4. Brightnesses measuring equal to the same measure
equal to each other and the sum of the measurements of the
parts is equal to the measurement of the whole.

In the opinion of the writer the flicker photometer should
be adopted as the standard instrument for making hetero-
chromatic comparisons in the standardizing laboratory.
Before, however, this can be done, the standard conditions
of illumination and field-size should be agreed upon, and,
most important of all, the normal luminosity curve of the
eye should be determined from observations on a large
number of individuals. This done, not only will it be possible
to determine which individuals should be chosen to make
such comparisons, but also, in virtue of the various qualities
of the flicker photometer, it will be possible to correct to
normal the results of any observer whose luminosity curve
is known. The next paper of this series will be devoted to
a discussion of standard conditions for heterochromatic

Photometry of Lights of Different Colours. 853

photometry and give values for the luminosity curve of the
average eye.

Attention may here be called to the fact that the solution
o£ the problem of heterochromatic photometry clears the
way for the establishment of a rational primary standard of
light flux, namely, a certain rate of flow of radiant energy
of maximum luminous efficiency*. It is hoped to use the
results of this study of coloured light photometry in a
determination of the luminous equivalent of the most efficient
radiation, a quantity which, in accordance with the above
suggestion, is identified with the rational primary standard
of light.

Physical Laboratory,
National Electric Lamp Association,
Cleveland, Ohio.
June 1912.

* "Energy Standards of Luminous Intensity," H. E, Ives, Trans. 111.
Eng. Soc. March 1911 ; " Luminous Efficiency," Elec. World, June 15,
1911.

From the Philosophical Magazine for December 1912.

Studies in the Photometry of Lights of Different Colours. — -
V. The Spectral Luminosity Curve of the Average Eye.
By Hekbert E. Ives.

ACCORDING to the results published in previous papers
of this series the flicker photometer, under certain
conditions, conforms most nearly of all photometric methods
to the requirements for a method of heterochromatic photo-
metry. Granting its adoption as the standard instrument
for this kind of photometry, there remain to be determined
the characteristics of the average human eye. Given the
satisfactory photometric method, and the standard eye to
use it, the measurement of the relative brightness of dif-
ferently coloured lights becomes a definite thing.

The present paper gives the result of an experimental
determination of the mean luminosity curve of eighteen
observers, sixteen men and two women, aged from 18 to 40
years. Since none of these were colour-blind or possessed
any known abnormalities of vision, the mean of their values
may be considered as that of an average normal eye. The
number of observers is sufficiently great to warrant the
belief that the mean thus obtained is sufficiently near the
absolute mean eye for all practical purposes.

The conditions holding during the measurements, the
reason for their choice, the details of the work, together
with the results, are discussed below under the several
headings.

Mr. H. E. Ives on the

Photometric Conditions.

Flicker Photometer. — The flicker photometer was chosen
for reasons made clear in the previous papers o£ this series.
It possesses the greatest sensibility, its results are most
reproducible ; by its use, things measured equal to the same
thing measure equal to each other, and the sum of the
measurements of the parts equals the measurement of the
whole.

Illumination. — An illumination of 25 metre candles was
chosen since, by the means described below, this was found
to correspond closely to the high illumination at which the
results of the flicker and equality of brightness methods
become the same. This is a practicable illumination for the
usual laboratory light sources and photometers ; it corre-
sponds to a comfortable working illumination for reading,
&c, and the changes in visual colour sensitiveness on going
to the still higher illuminations common by daylight are
probably small, perhaps negligibly so.

Size of Photometric Field. — A photometric field of 2°
diameter was selected ; that is, the smallest field used in
the previous work, for the reason that the changes in the
luminosity curve due to changes in illumination are least
with the small field. This field size, together with the high
order of illumination chosen, would permit considerable
latitude in the illumination without appreciable effect on
the result.

Bright Surrounding Field. — The small photometric field
was surrounded by a bright field of about 25° diameter,
maintained at approximately the same brightness as the
photometric field. This bright area, although previously
not found to affect the results of the flicker photometer to
an extent greater than the errors of measurement, was used
for the greater comfort which it gives when observing with
a small field. It is not an essential part of the scheme of
measurement, but for the sake of complete uniformity should
be used always, if at all.

Apparatus.

The apparatus was the same as in the previous work.
A Hilger spectrometer with a J x 2 mm. slit in place of
the eyepiece ; the light from the comparison lamp (4 watt
carbon), after falling upon a magnesium oxide surface, is
reflected into the spectrometer telescope from a first surface
platinized glass mirror arranged to oscillate and so form a
flicker photometer ; the diaphragm which limits the size of

Photometry of Lights of Different Colours.

855

the field is white and is illuminated by auxiliary carbon
lamps. The speed counter, slit mechanism, &c, have pre-
viously been described in detail. The light source whose
spectrum was measured was, as before, a tungsten lamp ;
the details of its use are given below.

Details of Measurements.

Energy Distribution in Spectrum of Light Source. — The
spectral luminosity curve which is desired is that of a known
energy distribution, from which the luminosity curve' of any
other distribution may be derived. For convenience it is
desirable to give the results for an equal energy spectrum.
Were it feasible to measure the intensity of radiation directly
at the eye-slit this would be the ideal measurement, since it
would at once eliminate the determination of various instru-
ment corrections. In the present investigation this was not
considered practicable, so measurements were made on a set
of four frosted bulb tungsten lamps whose energy distribution
was determined as follows : — All four lamps (previously
seasoned) were carefully colour-matched on a photometer
against a tungsten standard of 1*15 watts per mean horizontal
candle-power. Immediately before and immediately after
the use of each lamp on the flicker spectrometer it was
measured on a spectrophotometer (substitution method)
against a tungsten lamp which had previously been measured
against a black body of known temperature *. This latter
lamp had a visual energy distribution corresponding to a
black body at 2295° abs. The frosted lamps were compared
with it at four points in the spectrum. The distribution for
a black body,

14500

Jx = Cl\-5e at 9

was plotted as a straight line in the form

. J, 14500
lo3cV^= XT--1?***'

The spectrophotometer ratios were plotted (in logarithmic
units) against this straight line ; through these points
another straight line could be drawn if the new energy
distribution corresponded to another black body colour, as
is pretty wrell established. This was found to be the case,
and from the slope of this line the equivalent black body

* This standard of black body distribution was obtained and has been
maintained for this Laboratory by Dr. E. P. Hyde.

856

Mr. H. E. Ives on the

temperature of 2360° abs. was found for the lamp in question.
The distribution calculated for this temperature was in turn
corrected for the selective absorption of the prism, ground
glass, and lenses, determined spectrophotometrically, as well
as for the dispersion of the prism. Applying the final value
of the energy distribution to the readings, the results are
obtained for an equal energy normal spectrum.

Elimination of Artificial Pupil. — In all the previous work
an artificial pupil was used and the results were given in
terms of metre-candles illumination as viewed through this
1 sq. mm. aperture. In working with a spectrometer the
use of a small eye-slit is practically imperative. But in
practical photometry an artificial pupil of this size would
necessitate working at illuminations too high to be prac-
ticable with present illuminants if one had to attain the
retinal illumination called for by the investigation here
described. Were the pupils of all observers of the same
size under the same conditions, a reduction factor might be
obtained so that the luminosity curve could be found with
the artificial pupil and used for a corresponding illumination
with the natural pupil. Such, however, is not the case.

Fig. l.

h

a

Arrangement for securing the same working illumination
for all observers.

In view of these facts it was considered advisable in the
present research to have all curves made for a normal pupil
illumination. In order to accomplish this, the arrangement
shown in fig. 1 was adopted, a is the diaphragm limiting
the photometric field ; b is a small spectacle lens of focal
length ab ; c is the eye-slit or artificial pupil ; d is a lens of

Photometry of Lights of Different Colours. 857

focal length de ; e is a magnesium oxide surface illuminated
by the lamp h ; f is a lens of focal length ef. At g is formed
an image of the slit c ; the eye placed here sees the image of
the diaphragm a in the same plane as the edge of £, and by
moving the comparison lamp the field may be made of the
brightness of e. The auxiliary lenses are then removed,
proper correction made for the loss of light caused by the
various lenses, and the slit c used as before.

A test of the illumination used in the previous investigation
of the series — which in turn had been chosen to be in the
region where the flicker and equality of brightness method
had been found to agree, and where large and small field
agree, viz. 300 "illumination units" — showed that for the
writer's eye it was close to 25 metre candles. As this was
desirable from various standpoints, it was taken as the
constant illumination on e. Each 'observer was required
to find the artificial pupil illumination corresponding to
25 metre candles normal pupil, and his luminosity curve
was then obtained at that illumination. In this way the
results all apply to the standard illumination under ordinary
photometric conditions. It was found that the highest
illumination used was about twice the lowest. This range
would make no noticeable difference in the luminosity curve
with the illumination and field size used.

Details of Procedure. — The measurements of brightness
were carried out as in the previous work, by finding the slit
openings to match a constant comparison illumination. The
zero of the slit was found as follows : — By means of colour
screens the light of the comparison lamp was made to match
a certain wave-length (*59 /jl) ; then a series of three neutral
tint screens of known transmission were placed successively
over the comparison lamp side and the slit width obtained
for photometric match. These values when plotted against
the transmissions give a straight line passing through the
effective zero. This method proved very satisfactory.

The calibration for wave-length was provided for by having
the eye-slit adjustable sideways by a milled head ; a helium
tube was placed behind the tungsten lamp under measure-
ment so that it could be turned on at intervals during the
measurements and the setting of the drum checked. This
prevented any instrumental drift.

A difficulty was met with in carrying the measurements
down into the blue of the spectrum, namely, that the
necessary slit widths became altogether too great for sensi-
bility or accuracy. This difficulty was met by a compromise.
For the measurements at '50 fx and *48 fju neutral tint screens

858

Mr. H. E. Ives on the

of 3 and ^ transmission were used, so that these measure-
ments were actually made at lower illuminations than the
others. Since, however, the small field was used, and since
even these illuminations are only just getting into the region
of rapid change of luminosity curve shape (with large field),
the errors will be small. They are also in just the opposite
direction from the small errors due to the use of a wide slit
in this spectral region.

The manner of taking observations was to start at the
middle of the spectrum, then take observations back and
forth, from red side to blue side, working toward the ends of
the spectrum. This was found a desirable procedure, because
it gave the observers a chance to obtain practice on the
measurements with least colour-difference. At the end the
first two or three readings were repeated until a close check
was found. With some observers a check was obtained on
the first wave-length, while with others there was a difference
of several per cent, until the second or third wave-length.
The mean of both sets was taken where a difference was
found. Such differences are probably to be ascribed to lack
of practice at the start.

All the scale-readings were made by an assistant, who
watched voltages and held the speed constant.

Observers. — Of the eighteen observers, the majority had
never used a flicker-photometer, while several had never
before looked in a photometer of any kind. It is a striking-
point in favour of the flicker-photometer that its method of
use can 'be acquired so quickly that there is little choice
between the results of skilled and unskilled observers. The
former differ from the latter chiefly in the greater speed with
which they can make their readings. In instructing the
inexperienced observers the procedure was compared to
placing a blind man upon the side of a hill and asking him
to find the top. As he finds his position relative to the
summit only by stepping off in various directions, so the
photometrist locates the minimum of flicker only by oscillat-
ing the illumination (slit) until each direction of motion
increases the flicker. Standing still in either case is useless.
The correct speed was determined as that which made the
peak of the " hill " the sharpest.

Me suits.

The readings were first reduced to a normal equal energy
spectrum as described above. The resultant curves were
measured for area with a planimeter; then all were reduced
to the same area and their mean taken. This seemed on the
whole the fairest way to average the results, in view of the

Photometry of Lights of Different Colours. 859

fact that owing to differences in shape certain curves would
have less weight than others it' plotted in terms o£ equal
maxima or equality at any arbitrarily chosen wave-length.
According to the results of the paper just previous in this
series, the one thing common to all the curves would be
their area when the comparison light and the light dispersed
into a spectrum were identical.

The data o£ all observers are given in Table L, with their
mean. Table II. gives the mean values in terms of the

Table I.

Normal Spectrum Luminosity Curves of Eighteen Observers.

Observer.

•481

•498

•518

•537

•556

•576

•595

•615

•635

•655 [i

1. P.W.O.

3-4

5-9

1375

17-4

17-95

17-1

140

9-55

5-2

1-7

2. L.H.K.

4-15

7-1

155

18-7

18-6

16-5

12-2

75

3-65

1-15

3. E.J.E.

3-05

5-9

13-8

18-4

18-95

17-15

13-35

8-65

3-85

1-4

4. W.M.M.

3-6

7-4

15-2

18-45

19-05

16-65

12-45

7-75

3-8

1-15

5. M.D.O.

33

655

15-0

193

19-25

17-6

12-75

7-65

3-45

1-35

6. F.E.C.

2-3

5-05

13-9

17-9

19-1

1755

14-3

94

4-95

1-95

7. M.L.I.

325

5-45

12-75

17-8

18-9

17-8

137

9 05

4-55

1-9

8. M.L.

3-3

7-7

142

187

19-8

18-2

12-3

73

3-45

1-35

9. H.A.R.

3-3

6-9

14-2

17 7

17-8

17-2

13-45

90

4-65

2-00

10. L.R.Gl.

2-65

6-95

159

19-55

19-a

172

12-3

7-7

29

0-9

11. M.M.

3-9

7-2

14-7

17 35

18-5

16-65

13-15

8-05

340

1-2

12. C.F.L.

27

5-45

13-2

181

18-7

17*5

1415

9-2

4-9

1-6

13. A.J.S.

2-55

5-7^

J 5-2

19-05

195

17-45

135

8-25

41

1-4

14. A.W.

1-6

3*65

12-65

16-9

18-05

18-25

15-6

11-05

5-85

2-3

15. H.H.M.

2-6

61

14-85

18-0

19-45

17-8

1395

8-4

4-15

1-3

16. T.W.K

3-7

7-4

14-15

19 9

20-1

175

12-0

67

3-15

1-25

17. H.E.I.

30

6-1

15-35

18-75

19-3

17-4

13-45

8-25

3-9

1-5

18. G.C.

215

5-2

126

18-8

19-4

17-1

14-0

9-3

5-0

1-6

Mean

3-03

6-2

14-55

18-38

1903

17-47

1336

8 52

4-16

1-5

Table II.

Relative Luminous Efficiencies of Spectral Radiations.

X.

X.

•44 ii

•029]

•57 fx

-948

•45

•047

•58

•875

•46

•073

• -x-

•59

•763

•47

•107,

•60

•635

•48

•154

•61

•509

•49

•235

•62

•387

•50

•363

•63

•272

•51

•596

•64

•175

•52

•794

•65

•104

•53

•912

•66

•068]

•54

•977

•67

•044 I *

■55

1-000

•68

•026 J

•56

•990

* Extrapolated.

860

Mr. H. E. Ives on the

maximum unity, constituting a table of relative luminous
efficiencies of the spectral colours. In fig. 2 is plotted tiie

Fig. 2.

?/7^
if/

N V.

j

-if-/

if /

\ \,

* \

\ \

V-\

II

/

\ \
\ \
\ \

1:

l!
II i

— n

V

l'i
//.'...

/ //
/ //
/ //

? — v

I V

* B

b

\

\\\
\\\
>\ \

A

\\

«;

A

•40 -42 -44 -46 48 -50 -52 -54 -56 -58 -60 -62 -64 -66 -68 -70 71

Average Normal Spectrum Luminosity Curve of Eighteen Observers at 25 metre canllei

illumination of MgO surface.

Dashed line — . . Koenig's data, for his own eye, equality of brightness method.
Dotted line .... Thurmel's „ „ flicker method.

mean luminosity curve. Dotted in are the curves obtained
by Koenig *, for his own eye (equality of brightness method),
and by Thiirmel | (flicker method, also for his own eye).
The new curve, as it happens, is about midway in character
between the two latter.

Fig. 3 gives all the eighteen curves, each plotted separately
along with the average curve. Study of these shows their
range in position and shape. It will be noted that certain of
the curves are comparatively broad, others narrow, A rather
common difference is in the relative value in the green, i. <?.,
at '52 juL. Many of the curves would be alike except for their
flatness or prominence at this point. These latter differences
can probably be ascribed to differences in the pigmentation

* Data for High Illumination as reduced by Nutting, Bull. Bur. of
Stds. vol. vii. no. 2, p. 235.

f Annalen der Physik, vol. xxxiii. p. 1154 (1910).

Photometry of Lights of Different Colours. 861

of the fovea. There is besides a considerable range in
position, although the maxima of all curves lie very nearly
together, namely at *55 jl.

Fig. 3.

^ v..

'/ v\
1 \

/ ?- V

/ L.H.K. \

>\

It \

1 \

Jl w

/ s \

J M.P.C. \

l! r.t'.c. \

/ s \
/ ML- \

f 9 \

a h.a.r. V

/ i° \

J IRQ \

y '" V

I /3 \

J A.J.S. \

*

// \*

/ \\

i» V

A

I lb v\
/ T.W.-R *\

1 n \

1 HE I V

/ /fl \

^ v., i

Luminosity curves of all observers compared with the average curve.

862

Mr. H. E. Ives on the

Discussion.

Use of Luminosity Curve. — To the standard conditions of
heterochromatic photometry which have been outlined above
must now be added the use of the average eye as defined by
the data of Table II. Upon inspection of the curves of
fig. 3, it is clear that the individual variations are of such
magnitude as to prevent the use of more than a very few
eyes for coloured light photometry where any marked colour
difference exists. The extreme observers, for instance,
would measure a red light against a " white " light with a
difference of 100 per cent. These differences become very
much less when the light sources under comparison are any
of the ordinary illuminants, but some means of obviating
them is necessary in order to reach a complete solution of
the photometric problem. An approximation to the condition
of using a normal eye can of course always be reached by
securing the cooperation of a large number of observers, and
until each standardizing laboratory is prepared to obtain
luminosity curves of its observers and correct their photo-
metric work accordingly, this is the procedure to be recom-
mended.

The most rational manner of approximating to the average
eye is, however, by ascertaining the luminosity curve of each
observer in the laboratory and calculating the correction to
be applied to his results for the energy distribution under
measurement. According to the results of this investigation,
the total light is accurately the sum of the parts as measured
under the standard photometric conditions. It should there-
fore be possible to apply known energy distributions to the
observers' luminosity curves for certain physical conditions
of relative intensity (such, for instance, as equality at *58 fi),
and then from the relative areas of standard and test-lamp
luminosity curves in the case of the observers' eyes and in
the case of the average eye to obtain the correction which
would bring the observers' results to average.

This mode of correction was accordingly tested. A
" 4 watt " carbon lamp was measured on the spectrophoto-
meter, and by the above method its visible energy distribution
was found to correspond to that of a black body at 2080° abs.
The normal equal-energy spectral luminosity curves of the
two observers which varied most from the normal (14
toward red, 10 toward blue) were then multiplied at each
wave-length by the energy values for the 4 watt lamp (BB at
2080°), and for the tungsten lamp at 1-15 w.p.c. (BB at 2360°),
the latter values being taken arbitrarily as unity at *58 fi.
The areas of the four curves, measured by a planimeter,

Photometry of Lights of Different Colours. 863

indicated that observer 10 should measure the tungsten
lamp against the carbon as 3*3 per cent, higher than observer
14. An actual test, where the two lamps were measured
against a comparison lamp of intermediate colour, gave a
difference of 2*8 per cent. By this method of correction,
therefore, a difference of nearly 3 per cent, in the readings
of the two observers is reduced to J per cent. As these
differences are of the order of magnitude of the errors with
the planimeter and photometric methods, the test is taken
to show the validity and feasibility of such a method of
correction.

A possible and very attractive means of incorporating the
average eye into photometric measurement is the develop-
ment of some sensitive radiometer to supplant the eye. Such
an instrument so screened as to respond at the different
wave-lengths in accordance with the data of Table II. would,
if sufficiently sensitive, offer the most acceptable solution to
the problem. Perhaps the photoelectric cell will do this.

Summary.

This paper brings to a close the investigation on coloured
light photometry as previously laid out. The practical
result of the study has been to arrive at a choice of instru-
ment and of conditions best suited to this kind of photometry,
and to establish the characteristics of the average eye by
which such measurements are to be carried out. By con-
fining the actual comparison of differently coloured lights to
the standardizing laboratory, so that all practical photometry
is that of lights of the same colour, a solution of the problem
is offered through the use of the results of this investigation.
The results of the photometric method here advocated hold
for the average eye under the most important illumination
conditions. It is inevitable that correction factors will need
to be applied to these values whenever the effective illumina-
tions are widely different from that here adopted as standard.
But such corrections will apply to the less frequent and less
important conditions, that is, to ones where the loss in
accuracy involved by the use of more or less rough correc-
tions is of least importance.

Physical Laboratory,
National Electric Lamp Association,
Cleveland, Ohio.
August 1912.

1